the cosmic background radiation

RMSTA DEL NUOVO CIMENTO VOL. 17, N. 1 1994

The Cosmic Background Radiation. B. MELCHIORRI and F. MELCHIORRI

Istituto di Fisica dell'Atmosfera Piazzale R. Sturzo, 31 - 00144 Roma, Italia Dipartimento di Fisica Universit& ,La Sapienza,, Piazzale A. Moro, 2 - 00185 Roma, Italia

(ricevuto il 14 Ottobre 1993)

8 13 13 24 35 37 40 42 48 48 55 59 67 71 71 73 75 87 91 94

1. Introduction: the Cosmic Background Radiation, the goals and the limits of Cosmology.

2. George Oamow and the prediction of CBR. 3. Absolute measurements of CBR spectrum.

3"1. The discovery of CBR. 3"2. The decade of confirmation 1965-1975. 3"3. Considerations on CBR spectrum.

3"3.1. Astrophysical models for CBR. 3"3.2. Cosmological models for CBR.

3"4. The search for spectral distorsions: theoretical expectations. 3"5. Experimental techniques for searching CBR spectral distorsions.

3"5.1. Absolute radiometry of CBR. 3"5.2. The dipole anisotropy. 3"5.3. The search for CBR noise.

4. CBR polarization. 5. CBR anisotropies.

5"1. Early observations. 5"2. Semi-empirical description of CBR anisotropies. 5"3. CBR anisotropies and theories of galaxy formation. 5"4. Experimental problems in observing CBR anisotropies. 5"5. Measurements of CBR anisotropies. 5"6. Future plans: what CBR anisotropies can tell us and what they cannot.

1. - Introduction: the Cosmic Background Radiation, the goals and the limits of Cosmology.

Forty years ago in a BBC radio debate Gamow and Hoyle p resen ted the i r own ideas about the Universe. Hoyle was one of the th ree p romote rs of the Steady-State theory, together with Bondi and Gold. Oamow defended the idea of an evolving Universe. He was invited to coin a cr ispy phrase to condense his hypothesis in a nutshell . While Oamow was th inking at, Hoyle proposed the Big B a n g theory, with the obvious in ten t ion of laughing at the rival theory. This was the first t ime that such a n a m e was used (but for a different view, see Hoyle [1]). In any case, the appellat ion has outlived the Steady-State cosmology.

A review of the Big Bang theory is beyond the purposes of the p re sen t article. We will limit ourselves to what we cons ider the hea r th of Big Bang, namely the discovery and the investigation of the Cosmic Background Radiat ion (CBR). During the last ten years CBR has proved to be a powerful tool for cosmologists:

2 B. MELCHIORRI and F. MELCHIORRI

therefore is not inappropriate to open our article by giving a bird's-eye view of modern Cosmology with a special emphasis on the role of CBR, i.e. how the study of CBR could help in enlarging our view of the Universe.

Loosely speaking, the celestial objects we observe in the sky can be classed into pointlike and diffused sources: we are interested in counting them, in determining their space distribution, proper motion and shape: all these data may be achieved by measuring the spectral brightness and space distribution of the emitted electromagnetic radiations. Astronomers are far from having completed such a systematic survey, but even when the work will be finished the doubt will remain that the available data are insufficient for reconstructing the history of the Universe. Contrary to the famous phrase of the geologist Lyell, who revolutionised geology, The present is the key to the past, the present status of the Universe has a rather losely connection with the past, so that several antagonist theories, like Steady State and Big Bang easily survived to several tests based on the present status of cosmic affairs.

The basic ideas which make modern Cosmology possible have been exploited for the first time in two otherwhise wildly visionary papers by the French astronomer Flammarion[44] and the Italian Gesuit astronomer Secchi[45]. Flammarion (see fig. 1) combined the measurements of the speed of light (performed in France by Fizeau) with the estimation of the distances of a few nearby stars to conclude that the delay between the time of emission and that of arrival of luminous signals could be so large to open the possibility of observing the past of the Universe directly. Secchi, attempting to solve what we call today The Olbers Paradox, hypothesized that distant stars are receding so fast to shift their emission into the misterious ,,ultrared~ region, discovered by the Italian Melloni [57] (*).

The possibility of observing the past history of the Universe by means of IR and radio techniques is now well established. Still the reconstruction of our cosmic evolution is not easy: light from distant objects offers information on their own past: how this relates to the history of our and nearby galaxies?

The answer to the question depends on the amount of additional theoretical hypothesis we are ready to accept: a situation rather unusual in Physics. Let us present two examples, to better clarify the role of CBR.

i) Let us hypothesize that gravity dominates the Universe: perhaps a minimal theoretical prejudice about gravity that cosmologists are ready to accept, consists in what Barrow[2] called ,,the state of maximum ignorance~, i.e. the hypothesis that gravity is a metric phenomenon(**) . Under this assumption Hawking and Ellis [3] have proved that the existence of a singularity in the past is a consequence of CBR. The basic idea is the following. A Universe that at a certain epoch is enough isotropic and dense in matter and /or radiation is so close to Friedmann's models of general relativity that the singularity is unavoidable. The actual Universe is rather inhomogeneous, in terms of matter distribution; but it

(*) Sometimes the discovery of infrared is erroneously attributed to F. W. and J. Herschel, who first isolated near IR signals in Sun-light by means of a prism; both Herscheis concluded that the ~,heat-rays,, were of different nature than light and emitted by the Sun only. (**) There is a strong analogy between this hypothesis and the Einstein principle of equivalence, in the sense that the last automatically implies a metric theory of gravity.

THE COSMIC BACKGROUND RADIATION 3

- ~ i ! ! ~ i ~ l ~ l ~ --

,~'~ ~I:.,~. li~ ~!~'~i I L~a~ ~m.~'~e.

Fig. i. - In 1887 the French Astronomer Camille Flammarion wrote a prophetic paper entitled <,L'Univers Anterieur>~ in which for the first time the possibility is suggested of obselwing the past of the Universe by collecting the light from very distant stars. In the centre of the reproduced astronomical photo (one of the first realized) Flammarion has drawn a small white spot. In his intention this photo simulates the situation of our Solar System as seen by an observer billions of light years away: the primordial nebula is still collapsing and the planets are not formed. In this way an alien astronomer could study the past of the Sun. (Reproduced by L'Astronomie, C. Flammarion, edited by Gauthier-Villars, Paris, 1887.)


appears well uniform in terms of radiation, as the isotropy of CBR proves. The energy content of CBR is not enough today to exclude significant deviations from the isotropy in the past. However, CBR has a blackbody spectrum and its energy content increases with the red-shift Z like (1 + Z) 4. It follows that at Z _> 100 the energy density exceedes the threshold computed by Hawking and Ellis on the basis of purely geometric considerations. If the Universe was isotropic at Z = 100 as it is now, then the singularity is unavoidable. A short analysis of the cosmic story, proving that CBR has preserved its isotropy at Z---- 100, completes the proof of the Hawking-Ellis theorem on cosmic singularity.

Therefore, the first significant result of our analysis is that a measurement of the energy content of the Universe can provide fundamental information on the cosmic origin i f coupled with minimal theoretical hypothesis on the nature of gravity. For instance in fig. 2 we have summarized our knowledge about the radiation density. The threshold determined by the Hawking-Ellis theorem is also indicated. We may conclude that the Universe is borne because CBR is with us.

ii) We enlarge now our theoretical prejudice by adding the hypothesis that general relativity correctly describes gravity (*), then the Nel and Stoeger theorem applies (Ellis et al. [4]):

,,The observa t ions w e h a v e l is ted are n e c e s s a r y a n d su f f icen t to e v a l u a t e the m e t r i c a n d e n e r g y - m o m e n t u m tensor a long our p a s t n u l l cone u n t i l a s ingu lar - i ty is reached~.

In other words, the Nel and Stoeger theorem guarantees that the history of the Universe is known along our past null cone.

Encouraging as it is, this theorem leaves several problems unsolved, however. Perhaps the most unpalatable consequence is that we will never be able through observations to prove the cosmological principle (the Universe is isotropic at large). What we can test lies on our past null cone and we can say nothing outside it. The Universe could be uniform within our horizon and strongly inhomogeneous outside it, as in fact some models of Inflation suggest. Moreover, the theorem garantees the reconstruction of the cosmic history up to the singularity, and not in the singularity or ,,before~, it. In a sense, it states that we can investigate how the Universe started, but not why. This is a consequence of the classical character of general relativity.

From an observational point of view, one would like to be reassured about the strength of the theorem: the real observations are always limited in accuracy. What happens to the theorem if we take into account the instrumental uncertainties, the selection effects, etc.? Peebles and Silk [5] have suggested that we will never be able to exclude or confirm a cosmological theory beyond any reasonable doubt, due to the uncertainties in the observations and the degrees of freedom of the theories. The best we can achieve, in their opinion, would be a ,,degree of confidence~ or a figure of merit for each theory.

Even more crucial from an observational point of view is the problem of the trasparency of the Universe, since the Nel and Stoeger theorem requires a systematic survey of all the objects, no matter how distant they are. CBR photons are the

(*) General relativity is one of the various metric theories of gravity available in the literature.


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~ 2 . 7 K b l a e k b o d y

dust in \ clusters /

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energy enough for singularity

radio millimetric infrared visible X-ray I h I I I

6 8 10 12 14 16 log v (Hz)

Fig. 2. -A sketch of the major diffuse sky backgrounds as observed by an Earth's astronomer. Local backgrounds, like atmospheric emission and zodiacal light have been removed. The 2.7 K background and the X-ray background are believed to be extragalactic. The line indicated as ,,threshold of Ellis-Hawking theorem,, roughly represents the mini mum of radiant energy content which, if isotropic and present in the Universe at a red-shift Z_> i00, guarantees the existence of a singularity in the past, X-ray background is inadequate (clusters were not present for Z_> 20): it is the existence of 2.7 K background which makes the singularity unavoidable.

oldest available for observations and we immediately perceive the relevance of CBR studies. To give a more specific answer to the question, let us briefly summarize in fig. 3 the Big Bang story.

This figure represents a sort of schematic cartography of a ,plausible,, Big Bang Universe. We have no definite proofs that the real Universe coincides with that of fig. 3, still the figure is useful for our purposes in order to illustrate how the exploration of the Universe can proceed.

For the sake of simplicity, we have divided the past history into four sections. The first and oldest one is indicated by???? and consists in the so-called Planck epoch: formally, it could be defined by the time at which the radius of the horizon equals its Compton wavelength, that is tp ~- ( G h / c S ) 1/2 ~- 10 ~-43 s. At earlier times we have no adequate theories to guide us. The second epoch, classed as A, encompasses all the period dominated by radiation. Since we have an enormous excess of photons with respect to baryons (--~ 109 photons per baryon), the Universe remains ionized at very late epochs: the few photons in the


graviton opacity

quantum gravity

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waves end of electroweak ~ b a c k g r o end of grand unification primordial unification nucleosynthesis

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galaxy formation

Fig. 3. - A brief history of the Universe in terms of density, energy, temperature and horizon's size. The region C is currently explored by X, UV, optical, infrared and radio-telescopes. Region B is unkown, with the important exception of the last scattering surface, illuminated by CBR radiation. Region A may be explored for some extent by measuring CBR spectral distortions (up to Z-- 108) and CBR anisotropies at angular scales >_ 2-5 degrees (up to the Planck time, or the inflation time, if inflation occurred). (Adapted from a drawing prepared in Fermilab in 1986.)

high- f requency tail of a 3000 K blackbody are enough n u m e r o u s to keep hydrogen ionized. This second epoch (A), which we call for conven ience the radiat ion epoch, stops a round Z = 1000, when the hydrogen recombines . The subsequen t epoch (B) is often re fe r red to as the ,,medieval age,, of the Universe: it is in fact r a the r misterious. We know that s t ruc tures have been formed inside it, but no signals have been detec ted up to now. Finally, we arrive at the region C, ex tending f rom red-shift Z = 5 unti l now: this is the epoch commonly explored by astronomers, where single objects can be detected and counted.

Returning to our p rob lem of cosmic t rasparency, we note that in the f ramework of this naive Big Bang theory th ree surfaces of opacity are ant icipated. The pho ton ba r r i e r at a red-shift Z~- 103, the neu t r ino opacity at Z--~ 101~ and the graviton opaci ty (*) at Z-~ 108~. The th ree regions of opacity (photons , neu t r inos and gravitatons) are out l ined in fig. 3.

(*) Scattering between photons and electrons or molecules could be equally harmful to our purpose: its occurrence in the epoch B will be discussed later.


What emerges from fig. 3 is that in a logarithmic temporal scale our knowledge of the past Universe is rather limited. Conventional astronomy explores the last three orders of magnitude of a scale which extends for about 70 orders of magnitude down to the Planck time. We immediately realize the relevance of CBR. It allows us to observe the Universe at Z= i000. Moreover, since this last scattering turned out to be rather uniform, we can use it like a search-light lamp, to illuminate the structures in the red-shift range between i000 and 5. In a word, CBR has opened other four orders of magnitude to our possibility of observing the past Universe.

Figure 3 suggests an obvious question: how can we penetrate into Z>> i000? If the last scattering surface is a blackbody, every electromagnetic radiation cannot pass through it and the access at larger Z is forbidden. The first naive suggestion is that of dismissing optical techniques in favour of neutrino and gravitational waves astronomy. Cosmologists, however, believe that the situation could be more favour- able. First of all, it could happen that the last scattering surface is not a blackbody. Every injection of energy in CBR occurred at i08< Z< i000 would leave its imprint in the spectrum of CBR as a small deviation from the pure Planck curve. Therefore, we can explore the energy story of the Universe up to Z= 10s: unfortunately, for larger red-shifts there was time enough to thermalize every energetic phenomena. This situation justifies a careful search for spectral distortions in CBR.

The second possibility refers to the spatial distr ibution of CBR. Schematical ly, the idea is that we see on the last scat ter ing surface at Z = 1000 several regions which never went into contac t before. All the s t ruc tures larger than this scale have not been affected by physical processes and r ep resen t the si tuat ion as it was at earl ier times. In order to make these considera t ions more quanti tat ive we have to in t roduce a metr ic model for the Universe; let us use the F r i e d m a n n model in which the Universe is assumed to be isotropic at large (every di rec t ion looks similar for every observer) . In this model a physical dis tance dp be tween two objects scales like the expans ion factor R ( t ) : at early t imes R ( t ) o c t 1/2 and dp oct 1/2. In the same model the distance dH covered by a pho ton in the t ime f rom the beginning up to t scales like t. Deep enough in the past dH would become smaller than dp, no mat te r how small dp is now. This fact satisfies our first hypothesis that regions larger than dH at Z = 1000 r ema in grea ter t han it at previous times, simply because the ,(horizon,, dH decreases faster with t ime than any physical distance. If we use the Robertson-Walker metr ic , it is possible to compute the apparen t angular d iameter today for a region having the d imens ion of the hor izon at a red-shift z: in the case f2 = 1, the hor izon at t ime t has a p roper radius

2c (1) = ( ] +

Ho

and inserting this quantity into the distance-angular diameter relation we get

(2) sin = ~oZ + (f2o -- 2) [(K2oZ + 1) 1/~ -- 1]"

Therefore , if the densi ty of our Universe equals the crit ical value, the regions

8 B. MELCHIORRI a n d F. MELCHIORRI

casually disconnected at Z = 1000 correspond to angular scales of about 2 degrees in the sky. The angular distribution of CBR at ~ >> 1 ~ refers to a situation which remained unchanged since the beginning, i.e. from the Planck time t-~ 10 -4~ s.

This idea has been recently revolutionized by inflation: it predicts that isotropy may extend over all the angular scales thanks to the exponential expansion of the primordial space-time. Again, the study of CBR anisotropies at angular scales greater than one degree would permit to clarify this point.

The main conclusion of this section is summarized in the following: it is out of doubt that neutrino and gravitation astronomy will provide much better insight in the early times. At the present state of technology, however, CBR reppresents the most powerful tool we have in order to try to satisfy the conditions of the Nel-Stoeger theorem.

2. - George Gamow and the prediction of CBR.

The first time in Astronomy that an attempt was made explicitly to discuss the role of radiation in the early Universe is in a paper on primordial nucleosynthesis written by Gamow in 1948 [6]. Gamow's interest in Cosmology was triggered by the curious analogy between two rather different experimental results:

i) the dependence of the relative abundance of elements in the Universe on their atomic weight, as quoted by Goldschmidt [7];

ii) the dependence of the radiative neutron-capture cross-section on the atomic weight, as measured by Hughes [8] during a systematic search for materials suitable for nuclear reactors.

The two curves are shown togheter in fig. 4. Looking at them, Gamow in his own inimitable way immediately concluded that the early Universe started with a gas of neutrons: as protons formed from neutron decay, the neutron-capture reactions initiated to build up the elements in a sequential way. Gamow obtained a qualitative agreement between his rough theory and the observed abundance of elements, thanks to the similarity between the two curves of fig. 4. However, the theory was wrong for two reasons, at least: first of all the absence of stable nuclei at mass 5 and 8 would stop the sequential build up to light elements alone. Secondly, as Hayashi [58] has shown in 1950, one should compute the relative abundances of neutrons and protons by considering the elementary particles reactions, while a pure ,,YLEM~ of neutrons, as Gamow called it, cannot exist at all. In any case, the YLEM was the heart of the (1946) Gamow[9] proposal for a primordial nucleosynthesis in a cold Big Bang. The really new step introduced by Gamow in 1946 was the hypothesis that the primordial nucleosynthesis was a non-equilibrium process. In a Friedmann model for a dust Universe the expansion is governed by the amount of energy at the relevant epoch. In the early stages, when the density is large enough to allow nuclear reactions to occur (p >_ 10 -3 g cm -3, following Gamow) the expansion rate is so fast to reduce the density by an order of magnitude in less than one second. Therefore, Gamow concluded that: The conditions for rapid nuclear reactions existed only for a very short time, and the process was out of equilibrium.

During the following two years, Gamow added one important contribution: he


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Fig. 4. - A) Neutron capture cross-section vs. atomic weight, as measured by Hughes [8]. B) Relative abundance of elements in the Universe as estimated by Goldschmidt [7]: the vague similarity of the two curves induced Gamow to propose in 1946 the formation of the elements via a sequential capture cross-section [9] in an otherwise cold Universe. In 1948 he added the hypothesis that primordial nucteosynthesis was controlled by radiation, thereby opening the way to the prediction of CBR [6, 10].

no ted that the ra te of e x p a n s i o n (and the ra te of dec rease of T ) are domina t ed by the energy densi ty of radiat ion, which great ly exceeds tha t of m a t t e r [10]. There - fore, he p roposed that a t h e r m o d y n a m i c equ i l ib r ium holds be tween radia t ion and ma t t e r in the p r imord ia l Universe, a s i tuat ion r a the r different f rom the presen t .


As a consequence, the metric singularity of Friedmann-Lemaitre's models is reinforced into a hot singularity. In a modern view, the existence of thermodynamic equilibrium implies a significant semplification of the Physics in the early Universe: the total energy density can be written as

(3 ) Ptot ~--- ~ ( T ) PT'

where g (T) takes into account the total degrees of freedom of bosons and fermions and p~ is the radiation density. Gamow arrived at a similar conclusion by dividing first p into a mass contribution Pm and a radiation contribution p~. Then, he noted that the expansion rate of the early Universe, given by

: (4) H 2 (t) = 3

proceedes quite slowly unless Pv significantly exceedes Pro. If the Hubble t ime zH = 1 / H ( t ) is too long, all the hydrogen is converted into heavy elements. The amount of radiation density required to get the correct abundances turned out to be that corresponding to the case of thermodynamic equilibrium: i.e. cosmic matter at --~ 10 '~ K is immersed into a photon bath of a blackbody at the same temperature. For the radiation density Gamow [10] proposed the law

5 x 105 (5) flrad -- t ~ g cm->

He did not compute the present-day density, but the way was obviously paved. In the same year 1948 two Gamow's co-workers, Alpher and Herman, noted that the quantity prp~ 4/3 is conserved, as the expansion of the Universe proceeds [111. Since primordial/nucleosynthesis requires Pm -~ 10-6 g cm-a and pr ~-- 1 g cm , assuming a present cosmic density as given by Hubble of Pm (to) ~- 10 -30 g cm a, they obtained a present radiation density of about 10-3a g c m - a equivalent to the energy density of a 5 K blackbody. So, since 1948 a firm prediction for the existence of a universal blackbody radiation was available in scientific literature. Gamow[12] rederived the value of the CBR temperature in a paper (1950) published in Physics Today, giving a value of 3 K. The computation was repeated in 1953 [13] for a Danish journal (7 K) and in 1956 [14] for Vistas in Astronomy (6 K). Alpher and Hermann, also published these predictions several times (1948 [11], 1949 [15], 1950 [16], 1951 [17]). Some of them are collected in fig. 5. The 1951 paper was in a way unfortunate. Using a wrong estimate for baryon density they predicted 28 K and this number has been quoted sometimes to indicate the large degree of uncertainty in Gamow theory.

One point, which attracted the attention of Garnow, was the following: the radiation density required for primordial nucleosynthesis greatly exceeds the matter density. The origin of this huge amount of radiation was a mistery at that time. Garaow prophetically said that such a photon excess could possibly be explained by some still undiscovered property of matter. In 1967 Sakharov [18] hypothesized that these photons are the relic of the matter-antimatter annihilation occurred at much earlier times.


680

THE EVOLUTION OF THE UNIVERSE

By DR. G. GANOW ;eorge Wa~shington University, Washington, D~C,

N A T U R E Ocfober 30, 1948

IZera~mbering t ,h~ for the adiabatie expoamion of the r~l ia t ion T ~ 1][, we e~n integrate (2) into the fo rm:

~/~ 3 c ~ t l t 2-14 X 10 z~ OlC" (3)

For the me~s-dor~sity of r~d~tion we have : 3 l 4"5 X I0 ~

Pra4. =: 3~r,G " t ' = t ~ gm.crn.-L (4)

N A T U R E November 13, 1948 VoL , ~

Tho Lomporat, uro of *,ho gas a t 13~e titan of ~&te~ A, ASPHE~ ~olxle~l~bion wlm 600 ~ t{., and *oho tomt~ratRl~ in the ~OBERT ~-~ERMA~ universO at, the pros~nt t ime is fbund t o bo about 5 ~ K. II

Applie~t ~2hy~:ios Laboratory, Johns floph i~s University,

Silver Sprlag, ]~[&ryland. Oct. 25.

pHysICAL R E V I E W V O L U M E 75. N U M B E R 7

R e m a r k s on the Evolution of the Expanding Universe*, t RALPH A. ALPHER AND ROnERT C HERMAN

Applied Physizs Laboratory, Th~ Johns Hopkins U,ff:.ersily, Sidvcr @ri,*g, Moryh~nd (Received December 27, 1948)

In order to study how sensitive this modal is to lhe choice of densiti h idered the ..... ........ h # - - d • a~ fo l lowing add i t i ona l se t of d en s i t y v a l u e s which sa t i s fy Eq. (4 ) :

p = , ~ l . 7 8 X 10 -4 g/ctl~ ~.

p e ~ ' l g /cm*, (15)

p~,,~10 -s~ g / c m ~,

p,,,='~lO -3s g/cm ~.

T h e va lue o b t a i n c d for o~" in th is case c(mresponds a p r e sen t m e a n t e m p e r a t u r e of a b o u t I~ 0//r

REVI~.WS OF ~IOD~r~N PHYSICS AP RIL 1950

T h e o r y O~ t h e O r i g i n a n d m f l D i s t r i b u t i o n o f t h e 0

/ I RALPH A. ALPHER AND ROBERT C. I-[I~RMAN r ~

�9 / l I L / I A V ~ ' ~ " * * In raMels ,~f this type, energy is not conserved Equa- [ tions (91a) lnd (91b) may also be written as ~ . ~

p~p~-dt~=constant, (91c) ~ .

From Eq. (91c) one can then o.lculate p,,,, the present I density of radiation (the residual r~diation density I from the expansion alone), us I

. . . . . lO-~t g/oraL (14611

: : j t t .v;!u; of ......... pond ....... pe ...... no~o, I

PHYSICS TODAY AUCUST 1950

What happened to ylem in the first one thou

At the prewar epoch, h, which the density at real to, in the universe is atmuI 1o-:" R/Fill ~1 alld II: IelIIIICrAI~Ie i, only about 3~ t1,e den~hy ,d fad,: don {according t . the Stctan-J~llhxlll.atl0 ht~) 7- Io I'. (3)' ~ 6-1o 12 gg~/cm' ~ 0- i(i x: Z/el t l'hns even now the ms,s-dentil 3 o1 rmliation (c lated to m~s~nerg), r J:t~ ) iF on13 ai~ t~ctl~y dzntN smaller than thai ol .la~er

10. GeoTge Garaow

Fig. 5. - A collection of titles relative to papers of Oamow and his co-workers where the existence of CBR has been predicted since 1948. Particularly curious is Gamow's paper on Physics Today [12] where he predicted a temperature of 3 K, vely close to that observed fifteen years later: Gamow did not publish the computations he used for this estimate. (Prepared from [12-17].)

Gamow was never strongly interested in establishing the priority of his CBR prediction, being convinced that CBR was well below the possibil ity of any detection. Later on Alpher and Herman [19] have underl ined that the first predie-


t i on of CBR is in the i r 1948 p a p e r a nd no t in the p rev ious G a m o w ' s papers . Still, we t h i n k tha t it has to be a t t r ibu ted to Gamow, as eq. (5) c lea r ly shows.

G a m o w c o n s i d e r a t i o n s a re s u m m a r i z e d in a p lo t w h i c h G a m o w ca l led Divine Creation Curve, s h o w n in fig. 6.

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Fig. 6. The evolution of the Universe can be summarized in a few curves (Divine Creation Curves, following Gamow): The dependence of matter density and radiation density on the age of the Universe was first obtained by Gamow's phD student R.A. Alpher and published in his thesis (1950). About fifteen years later (1965) Princeton group rediscovered the same curves, as shown in the lowest part of the figure. (Adapted from [16].)


3. - A b s o l u t e m e a s u r e m e n t s o f CBR s p e c t r u m .

We can easily distinguish three epochs: i) the epoch of the discovery, ii) that of the confirmation of the Planckian character, and iii) the epoch of the search for spectral distorsions. We briefly discuss the three items in the following.

31. The discovery of the CBR. - Every attempt to reconstruct a scientific discovery is rather difficult: in the case of CBR it is even painful. If for discovery we mean observation and interpretation, it is clear now that this was not the result of the work of a single group.

Since our review is experimentally oriented, we consider as an adequate introduction to the problem the analysis of the technical developments which have made possible the early observations of CBR, independently of the fact whether their authors did recognize, or not, the cosmological nature of it.

It is beyond any doubt that among the various determining factors, the problem of extracting tiny signals from the noise was the first one to slow down any progress in radioastronomy until a satisfactory solution was found at the end of the forties.

As a matter of fact, already at the beginning of this century, enough sensitivity was reached in two fields of research to detect the effects of the noisily micro- scopic character of matter: spectroscopists interested in near-IR studies began to be limited in their observations by unwanted and random oscillations of the sensitive galvanometers employed to amplify the signals of thermopyles; electronic technicians were disturbed by the spikes present in the loudspeakers of radioreceivers. The last problem had serious consequences during World War I, when noisily transmitters and receivers made difficult and unsafe the transmission of military information and orders. The search for improving radioreceivers performances finally led to the fundamental paper of Nyquist [59], where for the first time it was shown that the noise spectral power in a resistor is obtained by dropping (v2/c 2) modes in the Planck formula, i.e. if the brightness IBB of a blackbody is given by (units of W cm -2 sr -I Hz -I)

(6) IBm= c2 �9 exp - -1 =

= 1.47- 10 .54 v 3- exp 1_11-1, the noise power of a resistor R at the same temperature is given by (units W Hz- 1)

(7) e2/R = PR = 2hv exp - 1 =

= 1 .3 . 1 0 - 3 3 v l e x p [ ~ l 8 " 1 0 - 1 1 V l _ ] l - I

It follows that the noise of R can be interpreted as the unidimensional case of the blackbody emission. This correspondence led the physicists to introduce two equivalent procedures for calibrating radioreceivers, namely by pointing the antennas toward a blackbody at a temperature To, or by connecting the input to

14 B. MELCHIORRI a n d F. MELCHIORRI

a resistor kept at the same temperature. In fig. 7 we have shown one of the earliest calibrations in terms of temperature produced by Lawson [39], a pioneer in the field, by connecting a 30 MHz receiver to a resistor kept at different temperatures. This plot, apart from its hystorical relevance, indicates two facts. First of all, the receiver output is proportional to the temperature of the calibrator, as expected, since the brightness of a blackbody is proportional to the temperature in the Raileigh-Jeans region of the spectrum. The second relevant point is the following: the straight line through the points does not intercept the origin: even in the absence of any imput the receiver shows a ,,temperature~ which is called the noise temperature of the receiver.

At the beginning of the sixties, the typical noise temperatures for radioreceivers were of the order of several thousand kelvin in the gigaHertz region. These huge values and their unavoidable fluctuations justify the sharp and negative answer that Alper and Hermann received by MIT technicians, when around 1955 they inquired about the possiblity of measuring a sky temperature of 5-10 K, as predicted by Gamow theory. As a matter of fact an enormous effort was made between 1940 and 1960 to understand the sources of noise and to reduce them.

Before proceeding, it is mandatory to clarify a point: a straightforward way to reduce the thermal noise is obviously that of cooling the receiver down to low temperatures, as indicated by eq. (7). This way appeared to be unpractical, however, because both the vacuum tubes and the mixers stopped working at few degrees below zero centigrades: and in fact it remained not feasible until low-temperature masers became available at the beginning of the sixties. In this respect it is curious to note that this solution, which was forbidden to electronic engineers, was in fact open to astronomers.

As a matter of fact, the first time that CBR has been observed (but misinter-

~9

O

O

temperature (K)

g

l I

I H

I 290 390

Fig. 7. - Reproduction of one of the first measurements of the noise temperature of a radiometer (operating at 30 MHz), performed by Lawson [39] in 1948. The radiometer input is closed to a resistor the temperature of which is changed. The extrapolation to zero temperature indicates the noise temperature of the amplifier itself.


pre ted) was in 1937, by Adams and D u n h a m [20]; they observed several faint opt ical-absorpt ion lines toward some molecu la r clouds i l luminated by the light of a star. These lines have been later identif ied as due to CH, CH + and CN ( D u n h a m [21-23]; Adams [24, 25]. See fig. 8 for an example of Adams detection. Mc Kellar [26] of Dominion Observatory in Canada from Adams data relative to the absorpt ion of CH and CN in an inters te l lar molecu la r c loud toward ~ Ophiuchi , derived in 1941 the exci ta t ion t empe ra tu r e of the rotat ional states to be a round 2.3 K, with no obvious source of excitat ion. Mc Kellar 's computa t ion assumed the rma l equi l ibr ium in order to evaluate the popula t ion of the various energet ic levels: a hypothesis highly quest ionable u n d e r the ex t r eme low densi ty of the in ters te l lar cloud. Moreover, he was unable to est imate the rate of exci ta t ion by collision. These uncer ta in t ies led, later on, Herzberg [27] tO quote the resul t in his famous book ,,Spectra of Diatomic Molecules,, by adding the c o m m e n t that the n u m b e r of 2.3 K has of course a v e r y res t r ic ted m e a n i n g . In the f ramework of our analysis we note tha t at first glance one can assume that the env i roment t empera tu re for such molecules is close to absolute zero: it follows that the study of the popula t ion of the first rotat ional levels allows to detect faint backgrounds at

CH line ~ . H line of CaII

~-Ophiuchi

P-Cygni

Interstellar lines of CH

MeKellar ~-Ophiuchi

~, Intensity ,~ Intensity A),

3878.8 1 3878.81 1 0.0 3886.39 3 3886.44 3 +0 .05 3890.23 2 3890.25 2 + 0.02 4300.29 > 6 4300.34 8 + 0.05

Fig. 8. - Measurements of Adams [24, 25] of interstellar CH toward the Star {-Ophiuchi: these measurements have been interpreted by Mc Kellar [26] as due to vibrorotational transitions. From the relative population of the states a temperature of 2.3 K was derived in 1941. (Adapted from [24, 25].) This was the first time that CBR was observed, although not recognized.


the excitation frequencies of the levels. Two of these wavelenghts are at 2.64 and 1.32 mm, close to the peak of the CBR; therefore, CN is excited by CBR and in fact Mc Kellar obtained from Adams data a ,,temperature~, of 2.3 K. Unfortunately, the poor knowledge of the astrophysical environment made it impossible to establish at that time whether this value represented the noise temperature of the CN-receiver (in this case the external background had zero temperature) or at least part of it was originated by a source outside the cloud. These results have been correctly attributed to CBR excitation only in 1965, by Field et al. [28].

Returning to the problem of extracting tiny signals from noise, the solution came from two independent sides almost simultaneously around 1946. Golay [40] proposed to improve the performances of his infrared pneumatic detector (the so-called Golay Cell) by adding a clever electronic amplifier based on ,,synchronous detection~; Dicke[29] proposed to improve the performances of a radioreceiver in the same way. Dicke fully analysed and discussed his technique which is now known as lock-in detection. The basic idea of lock-in detection is that of coding the signal in such a way to facilitate its extraction from the thermal noise of the receiver. In the early experiments of Golay and Dicke, the coding was accomplished for by modulating the incoming radiation by a rotating chopper at a frequency f0. Therefore, the radiation entering the receiver can be represented (in the case of sinusoidal modulation) as a signal AS= AT(AI)sin(9ot, where T applies for radioreceivers and I for IR detectors and the quantities AT, AI represent the difference between the source temperature (brightness) and that of the rotating chopper's blade, and (9o is the pulsation of the modulation ---- 27cf o. Synchronous detection is obtained by multiplying tI~e signal by a reference generated via a transducer applied to the rotating chopper, which can be written as R -- A sin (9o t, where A is a constant which can be set equal to 1 for the sake of simplicity. The product P--RAS becomes P--AT(AI) sin2 (9ot. When integrated for a time much longer than the modulation period T >> 2~/(90, the output of the receiver will become a d.c. signal proportional to AT(AI). The effect of this procedure on the noise can be easily understood if the noise is represented in terms of a Fourier series, like N--E~a~sin((git+ ~): all the terms, after multiplication by R and integration, tend to zero with the exception of that corresponding to (9~----(90: in this way a significant improvement in the signal- to-noise ratio is obtained.

The exact amount of improvement was first computed by Uhlenbeck [41] and it turns out to be

TNF (8) AT= (AgoT)I/~2,

in which TN is the noise temperature of the receiver, F is a form factor which takes

into account the shape of the modulation (close to x//2/2), Aco is the bandwidth of the receiver in Hz, z is the integration time. For instance, in the case of the Dicke receiver, TN ~ 7.103 K, A ( 9 - 50 MHz, z-~ 2 s and we get ATe_ 0.5 K, which means that CBR can be detected in two seconds of observations with a signal-to-noise ratio of the order of 6. It is clear that lock-in techniques enormously facilitate the goal; they have in fact opened the way to modern radioastronomy.

A sensitive radioreceiver, coupled to a coventional radio-dish was employed in 1957 for a systematic survey of the galaxy around 33 cm by Leroux in France: fig. 9 shows the map he obtained. Pointing the radioreceiver well outside the


SEANCE DU I 7 JUIN ~957.

RAI)IOASTIIONOMIE. - - ,Noueelles obsercations du rayomzenzent du Ciel sur la

lo*zgueur d 'onde 33 em. Note de MM. JE,~-Fa*~'~o,s D~zmss% dxM~s L e e u ~ o x

et I~i,i,+ El+ l/oIlx, pr4sentde par M, Andr6 Danjon.

BO 7O 60 5o 4o

'.5 19

24 . . . . fOUars r_.~LACTIOUE ,

�9 CENTRL ~,~ 50URCE5 LOr,~USECS

"I UNtTs : 2,5 ? K

T> I O ? K

Fig. ].

2?ayom~ement d~ C'ie[. ];n d , ' h m - &'s r ( ,g i .ns quc ] 'on x ivn l dea l@t i r e , ]a b r i l l anee du Cie] pa rah , u n i f e r m e . ,",,n l'aVOllnlql?elll t.st dillicile i~ ll]CSlll'er ea r on l'observe supcrp(>d aux ell]]F, siitllS ]je;ql],:',)ll l, plUS iu lenxes de ] ' e n \ i - rOllrlelllenl eI a71 ]sl'uil ])l'Opl'C (]11 I,}Ccp|(qll'. ~O:" II)CSIIFI'S tlll{, t ou te fo i s

p e r m i s d,. m o n h ' e r quc la t e m p d r a l u r , , (h' br i l lam.c du Ciel es~ iufdr ieur , ' "~ 3" J< ~.I que ses v a r i a t i o n s d ' u n p,nim h un au l r e s,mi. inf~:rieur~,s ~'~ o,5" K.

Reproduction of page 50 of (Lemux's thesis).

En r ~ s u m ~ 0 on a t r o i s ~ q t ~ t i o n s dormant T c :

V o f f i 0 t37 ffi 138 - 0 . 4 8 5 T c p T c ffi 2 ~

(25) V o = 5 50 = 5 1 , 3 - 0 . 4 8 5 T e * T c f f i 2 ~

V o - - 3 2 1 5 = 2 1 8 - G , 7 7 T c ' T c s 3 0 9 " K .

En N i t . o n d e v r ~ i t d~duire , de p l u s i e u r s ~kluations de ee g e n r e , l e s coelT.icie4tts Ilk.p. p~. pt, e t T e . M a i s la bo(me r d e s v a - l e u r I olblcnucs po ur T c m o n t ~ que l e s v a l e u r s p r i s e s poar r 1 6 2 coefficient, '; son t c o r r C c t e s a v e r mae bo nne a p p r ~ n a t i ~ m . $ i on d i m l m ~ i t le c v e f f i c i e n t 1 / k On o bt i endra i t d e s v a l e u r s n ~ g a t i v e s pour T o , q u e U e I ~ so i en t l e s v a - l eurS p r i s e s po ur p' e t p " qui in terv iennent de fa~o~ dIf f~rente clans l e s 3 ~quat ions prdc~denteSo le c o e f f i c i e n t p' in tervenant n o t a m m e n t de fa~on o p p o s ~ e clans l e s d e u x d e r n i ~ r e s ( 'quat lces . De m ~ m e . turn augmenta t ion de I / k de q u e l q u e s po ur c e n t do nnera i t de s v a l e u r s de T c incoh~rente~ . E n f i n . un c o e f f i c i e n t de r ~ f l e c t i o n du s o l non nul donnerai t T c < 0 .

I1 e s t d i f f i c i l e de d ~ t e r m i n e r l ' e r r e u r s u r eerie v a l e u r de T c . b a - s ~ e f u r la c o h e r e n c e de d i / f ~ r e n t e ~ m e s u r e s . N o u s p e n s ~ clue l ' e r r e u r a b - s o l u e doit ~ t re de l ' o r d r e de 2" K. en prenant :

Fig. 9. - In the upper part of the figure we have reproduced the Milky Way map obtained at 33 em by Leroux et aL in 1957 [31]: in that paper an upper limit of 3 K for the sky background is quoted. But, as shown in the lower part of the figure (a reproduct ion of p. 50 of Leroux thesis), these measurements have been originally quoted as a detection at the wavelength of 33 cm. (Courtesy by gncrenaz [32].)


galactic plane, Leroux found a sky temperature of (3 _ 2) K: this rather interesting result was later published as an upper limit of 3 K [31]. A page of Leroux thesis is reproduced in the lower part of fig. 9. Also Leroux estimated an upper limit at CBR anisotropies around 1 degree of angular scale (AT_< 0.5 K).

A sensitive radioreceiver is certainly fundamental to detect the faint CBR, but is not enough. Spurious radiation, coming from antenna's sidelobes, can in fact completely mask the cosmic radiation. A real improvement on this subject started around 1955, when Bell Telephone Laboratories (BTL in the following) became interested in the study of the feasibility of providing long-distance communicat ion facilities by means of reflection from orbiting satellites. This led to the partecipa- tion in NASA's Project ECHO, the general features of which are illustrated in the scheme of fig. 10.

A large reflecting balloon was inflated and placed in an almost exactly circular orbit with an inclination of 47.3 ~ providing a period of mutual visibility for Jet Propulsional Lab (JPL) and BTL of about 20 minutes. Radiosignals, sent via a powerful transmitter from one station, are reflected by the balloon and detected by means of a large, clean radiotelescope. To this purpose, BTL developed a giant horn-antenna 20 x 20 feet with an overall length of about 50 feet, coupled to a low-noise maser amplifier, cooled down to liquid-helium temperature. The system was the best designed and the most sensitive in the world for its intended use in communicat ion research (see fig. 11).

The basic scheme of the horn-antenna is shown in fig. 12: it consists of a piece of paraboloid, accurately shielded all around by flat shields. The sidelobes are substantially reduced, as one can see in the lower part of fig. 12, where measurements are shown as obtained by means of a powerful transmitter located at

�9 ,,~ ECHO i .~ balloon

I

. " d "

~ : . . - , - [ , ~ O.aeo 85 receiver 600 km o

radar ,,,~-: in ~ w " tracking ' ~ 1 r e c e i v e r 10 kW . . . . . . . = : ~ - . - . . _ 20'x20' horn *r . . . . i *§ transmitter ~ N R L ~ ~ . . ~ N t ~ . . . . . . . . . . .

~ ~ receiver

Goldstone Holmdel California

Fig. 10. - Scheme of ECHO satellite experiment: a large reflecting balloon was set in an almost circular orbit in order to test the possibility of radio-communication coast-to-coast from JPL Goldstone Lab. in California to BTL in Holmdel. BTL Lab. developed a special receiver consisting in a horn-antenna and a liquid-helium-cooled maser, operating around 2 GHz of frequency. This receiver was later employed by Penzias and Wilson in their discovery of CBR. (Adapted from [33, 34].)


Fig. 11. - Photo of the 20' x 20' horn-antenna of Bell Telephone Labs. in Holmdel: the big wheel allowed changes in elevation from horizon to horizon.

different angles with respect to the antenna axis. The Earth's radiation entering via the spillover lobe at 70 ~ produces an excess of noise at the receiver, even in the absence of any radiation in the line of sight. Its amount is very small, however: with an attenuation of more than 35 dB (i.e. ~- 10-as), the expected temperature noise of the antenna would be less than 0.i K.

The amplifier was a three-level solid-state maser, which employed a microwave pump signal to alter the thermal equilibrium of a paramagnetic salt in such a manner that the absorptive medium becomes emissive when stimulated by radiation at the signal frequency: microwave amplification is thus obtained. A clever design is needed to efficiently couple the microwave fields to the paramagnetic salt. For a detailed description of the BTL amplifier see, for instance, De Grasse e t at. [42].

As a first step in the BTL program, a small prototype of the antenna was realized and studied by Hogg and Semplak [43]. During October 1960 they employed this system, operating at 6 GHz with a field of view of 1.75 degrees, to study the atmospheric emission. This was the first time that CBR could have been detected, because the receiver was sensitive enough (the quoted noise was of


15.5 K) and the antenna had very reduced sidelobes. The analysis of the data carried out by the authors is at the basis of all the measurements of CBR. The signal of the system, expressed in terms of antenna temperature, is given by

(9) T t = e [TCB R ~ - Tat m -~- Tantenn a -J- Twavesuid e -~- Tmaser] ,

m~in h ~ m

sp: lot

spi l lover lobe

0 - 1 0 - : i .-:-:.1 ~ - ~ - ' - ~ . . . . . ~ - - L = - - . ~ . :

- 4 0 - VV' ' ~ vv ~%%,2"~ ,h ,~,, ^ - ~. :: ..... i ...................... , . . . . . . . . . . . . . . . . . . . . . . . . . . I ......... J ......... I . . . . . . . . . . . . . . . . . .

330 3 4 o ~ o o lO 20 36 4o 50 60 70 so' 9o lOO O a (degrees)

~ - 5 o i 1 , i I

-55 ' I ~ i - 6 0 i I ~ i i

50 55 60 65 70 75 80 85 0 L (degrees)

Fig. 12. - U p p e r panel : s c h e m e of t he h o r n - a n t e n n a . It is a pa r t of a large parabo lo id : l a te ra l sh ie lds p r e v e n t spur ious rad ia t ion e n t e r i n g in t he sys tem ou ts ide the n o m i n a l b e a m width. I so t ropic level -- 43 dB. Lower pane l : angu la r r e s p o n s e of t he a n t e n n a , as m e a s u r e d by m e a n s of a t r a n s m i t t e r loca ted in f ron t of t he a n t e n n a at d i f fe ren t angles . T h e sp i l lover lobe is s tud ied in detai l in t he lowest pa r t of t he graph. Ea r th ' s r ad ia t ion e n t e r i n g via t he spi l lover lobe d e t e r m i n e s t he a n t e n n a t e m p e r a t u r e noise. - - Measu red data, �9 c o m p u t e d data. (Adapted by Crawford et al. [34].)


where the symbols are obvious: Twaveguide refers to the noise added by the waveguide connecting the antenna to the maser amplifier. Due to the different path through the atmosphere at different elevation angles we can write

(10) TcB ~ + Tat m = 2.73 exp [-- ~ sec O] +Teff [1 -- exp [-- ~ sec O]].

If the atmospheric transmittance is high, the first term is almost constant as the antenna is tipped at various elevations and 2.73 K of CBR is formally added to the other constant terms of eq. (9). For instance, Hogg and Semplak found that if system noise = Tantenn a -~ Twaveguide "~- Tmase r = 15.5 K the data describe perfectly the atmospheric emission, as shown in fig. 13.

The chances of detecting CBR are thus related to the precise knowledge of the ,,system noise,s. A more detailed analysis of this noise was carried out on the final antenna by Ohm [33]: the noise budget is summarized in table I, taken from the original Ohm's paper.

First of all, we note an overall uncertainty of _ 3 K which makes by itself CBR temperature marginally detectable at 1 standard deviation. Moreover, the antenna noise of (2 _+ 1) K estimate was based on the temperature ,,not otherwhise accounted for,,, leaving room for a sky excess of the same order.

The above uncertainties are not taken into account in the plots of signals obtained at various tipping angles, as shown in fig. 13. This fact led Doroskevitch and Novikov [35] to conclude that the data were in a very good agreement with the atmospheric emission, leaving room for less than 0.2 K for the extra-atmospheric sky temperature. Particularly misleading in this respect was the conclusion of Ohm's [33] paper on the estimate of the sky temperature: he provided a zenith temperature of (2.3 _+ 0.2) K with a theoretical computation for the atmospheric zenith emission of 2.4 K. Only a careful inspection of Ohm's paper explains this result, which was obtained after removing the constant terms in the radiometer output.

The above analysis led us to conclude that a sensitive radiometer plus a low-sidelobes antenna are still not enough to allow a believable detection of CBR. All the previous experiments lack a good reference source the temperature of which is known with enough precision to provide a safe calibration of the system. This was the main contribution of Penzias [46], who realized a blackbody operating at liquid-helium temperature, by means of a wave guide immersed into liquid helium and terminated with a cone of good radiowave absorbing material. The wave guide was made by copper in order to maximize the thermal conductivity and

TABLE I. -- Sources of system temperature.

Source Temperature (K)

Sky (at zenith) Horn antenna Waveguide (counter-clockwise channel) Maser assembly Converter

(2.30 + 0.20) (2.00 _+ 1.00) (7.00 + 0.65) (7.00 +_ l.OO) (0.60 _+ 0.15)

Predicted total system temperature (18.90_ 3.00)


10 a

r - - .

0 9

0 9

101

0 10 Z e n i t h

1 10 ~

0 2 0

_h J

. . . _ , - - i

S"

20

H

i . - I �84

5O

3 0 4 0 5 0 6 0 7 0 ( d e g r e e s )

i . . . . . i

,~

I

70 80 82 88 degrees

7 P / !

?

/ t

Y

I a ) 80 9 0

i

I i

i �9 , / ' i P

b)

Fig. 13. - These two plots of radiometer outputs v s . the elevation angles have been misinterpreted by Doroskevitch and Novikov [35] in their search for CBR. The authors of the plots have included in the system noise all the possible constant excesses: the 2.7 K excess due to CBR was also included. Since this point was not clearly stated in the papers [33, 43], Doroskevitch and Novikov were led to conclude that no other sources of radiation were present apart from the atmosphere, a) f = 6.0 GHz, ToB ~ < 3 K [43]; - - - theoretical sky teraperatures at 6 KMc for standard Earth atmosphere; �9 measured sky temperatures for 7 Oct. 1960. Ground temperature 58 ~ water vapour density 5 g/m3; - - effective input temperature, b) f = 2.390 GHz, TcBR < 3 K [33]. (Adapted from [33, 34].)


to r educe the t h e r m a l grad ien t across it. For a view of the ca l ibra t ion source , see fig. 14a) and b).

A very s imi lar source was in cons t ruc t ion at P r ince ton , a r o u n d 1963, in the group headed by Wilkinson, with the a im of sea rch ing for CBR. The s tory of the

r

.... �9 n h : h : : ~ : : n s f e r

a)

Fig. 14. - The liquid-helium-cooled standard realized by Penzias [46] in order to have a precise calibration of the BTL receiver. The wave-guide was terminated by a piece of highly absorbing material: few small holes allowed the last part of the waveguide to be filled by liquid helium in order to stabilize the temperature. A tilted mylar film closed the upper part of the waveguide which was vacuum tight. The good performances of this reference source have been crucial in making Penzias and Wilson confident in their results. (From [46].)


measurement of CBR by Penzias and Wilson and its interpretation by Princeton Group is written in almost all the reviews dedicated to CBR and we will not repeat it here [36-38].

Two lessons can be learned from the discovery itself. First of all, it is now clear that the discovery was made by chance, but it is also true that it was possible because Penzias and Wilson employed the most advanced radiometric system for their time: three new fundamental improvements in radioastronomy were employed. A new telescope, having very reduced sidelobes, a new method of differential radiometry, based on the so-called Dicke switch, and a new absolute calibration standard, cooled to liquid-helium temperature. The lack of any of these items would have made the detection of the CBR impossible. For instance, Dicke has employed a radioreceiver with its switching system, since 1946, but the lack of c lean sidelobes and of a cold well-designed re fe rence source allowed h im jus t to pu t an uppe r limit of 20 K to the sky brightness. Ohm used the same te lescope as Penzias and Wilson did, a Dicke-type receiver but not a cold r e fe rence source: the unce r t a in ty in his measu remen t s was just at the level of 1-2 K, too large for making h im conf ident in the sky t empera tu re he detected.

The second lesson is the following: exper imenta l physicists are s u r r o u n d e d by effects which h a m p e r the i r searches. Some of these effects can conta in fu n d am en - tal physical implications, m a n y are just spur ious dis turbances. The key point for a new discovery lies in be tween the intui t ion of what effects are in t r ins ical ly important , and the ost inat ion in trying to e l iminate and u n d e r s t an d what we cons ider spur ious cases. After a few tests, Ohm [33] decided that a not well- identif ied ,,excess of noise,, was p resen t in his system and left to o ther physicists the goal of unders t and ing and el iminat ing it. Penzias and Wilson dedica ted more than one year of a t tempts to avoid all the possibile causes of noise and, finally, r e a ched the conc lus ion that it or iginated f rom the sky and not f rom the i r ins t rument .

32 . The d e c a d e of conf irmat ion, 1965-1975. - In order to fully apprec ia te the efforts car r ied out by several groups to conf i rm the P lanckian cha rac t e r of CBR, few technica l words are needed.

CBR is a diffuse radiation, there fore its na tura l units are the spectral brightness I v (W Hz -1 m -2 sr - I ) or I~ (W gm - I cm -2 s r - i ) . For a pu re b lackbody the two quanti t ies are given by the Planck formulae

2hv s 1 (11) I~ dv - - -

c 2 exp [hv/kT] -- 1 dv,

2~c2h 1 (12) Iz d)[ - - - d~,

~5 e x p [ c h / ~ k T ] -- 1

where

2~zc~h = 3.74 W ~ t m 4 c m - 2 , c h / k = 1.438 �9 1 0 4 ~tm K.

The two br ightnesses peak at

2.897 0.568 cT 2 m a x - - ~m K, Vraax = Hz.

T 2.897


In the so-called Rayleigh-Jeans region of the spectrum, where hv << kT, the spectral brightness is given by

2v2kT (13) L - c ~

If we employ a radioreceiver to measure this brightness we have an interesting and useful consequence: being a coherent detector, a radioreceiver is sensitive only to radiation having a definite phase with respect to the local oscillator. Therefore it rejects the radiation out of the central maximum of diffraction. It follows that the throughput A x Q (area by solid angle) of a radioreceiver is diffraction limited and approximately equal to j%s.

The power incoming in the detector is obtained by multipling eqs. (ii), (12) by A x Q: therefore, the dependence on the frequency disappears and the output of the radioreceiver is proportional to the temperature only. We can calibrate our instrument in terms of temperature and use it like a termometer. One has to stress that this situation holds only in the Rayleigh-Jeans part of the spectrum. If we use our radio-termometer in the Wien region, we get a temperature which is significantly lower than the true thermodinamic temperature of the blackbody. We can still convert this temperature (called antenna temperature) into the thermodynamic temperature through the law

(14) TA = r h c / 2 k T

exp [hc/,~kT] - 1"

For a 2.7 K blackbody eq. (4) has the numerical value

(15) TA = 2.7 5 .28 /~

exp [5.28/2] -- 1'

where 2 is in ~m.

In order to measure the brightness of a source, we need an absolute radiometer: the ideal radiometer would consists in a well-calibrated detector. Several pratical problems arise, however. Every radioreceiver has a noise temperature of several hundred kelvin which is slowly changing in time, over which it would be extremely difficult to detect the small 2.7 K increase due to CBR.

A second problem related to the previous one arises with the linearity of the detector and the stability of the electronic gain, if one has to measure a tiny signal over a huge offset. In order to overcome all these problems the best arrangement is that of using the detector as a zero instrument. The sky radiation is compared with that of a reference source, the temperature of which is changed until a zero output is recorded: at this point, if the reference source is a blackbody, its temperature coincides with that of the sky. Since the detector is operating near to the zero, its linearity is guaranteed: moreover, if we make the comparison between sky and reference source frequently enough the detector offset has no time to change within each measurement.

In conclusion, the best absolute radiometer would consist of three items:


a) a detector having a good sensitivity and stability;

b) a reference source the emissivity and temperature of which are well known;

c) a switching system which interchanges several time per second the sky radiation with that of the reference source.

Such a radiometer is still very difficult to realize: in order to have the detector operating as zero-detector one should have a reference source operating near 2.7 K. This is not difficult to achieve, by pumping on liquid helium: but in order to pump on the cryogenic liquid it should be enclosed in a vacumm-tight system, the window of which would radiate an unknown amount of power. Therefore, one is forced to work at slightly higher temperature, like that of 4.2 K, relative to liquid helium at ambient pressure. Even this solution is hard to mantain for long times: the ambient radiation coming inside the liquid-helium container has power enough to boil off huge amounts of the expensive gas in a few minutes. Therefore, one is forced to search for another less expensive reference source which is time by time compared with that at liquid-helium temperature.

We are now in a position of rewriting the Fundamental Equation of Radioreceivers, similar to eq. (9) of Hogg and Seinplak [43]. A sketch of a typical operating system is shown in fig. 15. The sky radiation is represented by three components, which are expressed in terms of antenna temperatures:

T~tm = atmospheric emission at zenith,

TcBR = CBR radiation at the frequency of operation,

TQa~ = galactic diffuse background at the frequency of operation.

The disturbing radiations are

T~ound = radiation emitted by the surrounding ambient and entering in the field of view,

Twan = radiation emitted by the walls of the reference source, which are at higher temperature than the liquid-helium,

Thorn = radiation emitted by the collecting optics of the apparatus,

Toffset = radiation arising by the imperfect switching and by the operating temperature of the apparatus.

The primary reference source is represented by the liquid-helium blackbody: since it operates for few minutes, a secondary reference source is represented by the sky itself at the zenith. A typical sequence of measurements consists in keeping the horn A of fig. 15 fixed and slowly rotating the plane mirror in front of Thorn to record the atmospheric emission at various elevations. At the beginning and at the end of each set of observations the horn A is directed toward the primary reference source to ,make the instrumental zero,,. The output of the radiometer is proportional to the difference

(16) T ~ -- Tco~d = TcBR § Tatm § Toal + Tground - - (Tile § Twall) § AToffset,

where Tsky is the total radiation coming from the sky and Tco~d is the total radiation


n

rotating ~ , ~ : : [ [Tatm+TeB? + T G a l l - - bearings ] i

i- -~ corrugated I i ..... / z / -: ' horns <-=7

Dicke / ~ switch -~ ~_ Tho~n~ ~ '~ : :

.Sz /

r e c e i v e r / A ~ ', . . . . . . . . . . . . . . .

absolute reference TH e I ............ aluminum-coated] I ~ j a t LHe temperature H~ T~all m y l a r ~ _ ~ . ~ . \ . - - - LN -!--

tank:

windows

eccosorb

7." . . . . .4

Fig. 15. Sketch of a radiometer designed to measure CBR spectrum. While one of the two antennas is receiving the radiation from the sky at different zenith angles, reflected by a rotating mirror, the second antenna (indicated with A) points either to the zenith or to the the absolute reference standard, via a rotation of the entire assembly. The reference is realized by means of a liquid-helium Dewar and a large Eccosorb panel immersed in it. The scheme is that employed in the White Mountain collaboration.

coming from the primary standard when the horn A looks down in it. AToffset represents the change in the offset when the horn A is rotated, essentially due to the mechanical stresses.

The presence of many additional terms in eq. (16) with respect to the interesting one TcBa rises the question how reliable could be such observations and what are the terms posing the most serious limitations.

It is now widely believed that at wavelenghts 2 _< 10 cm the correction for the atmospheric diffuse background is the major source of uncertainty. For 10 cm _< 2 <_ 20 cm, the source of uncertainty is the correction for the temperature of the walls of the reference source Tw~H. For 2 _> 20 cm the galactic emission TQ~ is the principal cause of systematic errors.

At the time when Penzias and Wilson published their result, already few upper limits were available at slightly different frequencies: the already quoted result of Hogg and Semplak of about 3 K at 6 GHz, the upper limit again of 3 K of Leroux [31] at 0.9 GHz, and the upper limit of 16 K at 0.4 GHz of Pauliny-Toth and Shakeshaft [47], the last one being the only one quoted by Penzias and Wilson [30]. These data by themselves already represent an impressive set in favour of the existence of CBR. Immediately after the publication of the results by Penzias and Wilson, a rapid increase in the number of experiments has been

28 B. MELCHIORI~I and F. MELCHIORRI

recorded. It is beyond any doubt that the largest contribution was that of the Princeton Group, headed by Wilkinson. Within 5 years this group alone covered the frequency range from 9 to 90 GHz with 6 different radiometers [57-60]. The average result of their work was

(2.63 • 0.10) K,

a value not only consistent with modern results, but so accurate that even the most recent measurements are unable to add a significant improvement. In fig. 16 we have compared Princeton results with the most recent results at the same frequencies obtained by the so-called White Mountain Collaboration. It is clear that very limited progress has been done and the improvement in accuracy is marginal.

Some of the instruments employed by the Princeton Group are in fig. 17. As the frequency of operation increases, the emission by the atmosphere becomes important. Therefore the observations at highest frequencies of the Princeton Group (90 GHz) have been carried out by means of an airborne instrument. Unfortunately, the space available on board of the plane (a small executive Lear Jet) was not enough to allow the use of an helium-cooled source. Therefore, the instrument was calibrated immediately before and after the flight, while a liquid-nitrogen source was employed in flight, as shown by the sequence of fig. 18. The experimental difficulties justflies the large bar error for these measurements.

As a matter of fact, the problem of atmos )heric emission was never fully

4.0

~ . 3 . 5

0)

4~ 3.0

2.5

2.0

I I I l i l l l l V-7 I I IIIII L111111 I I ]

10 -I i0 ~ 101 10 2 10 8

frequency (GHz)

Fig. 16. - Early Princeton results (dotted line) compared with more recent measurements of White Mountain Collaboration: despite the fact that more than 15 years divide these observations, it is clear that the improvement in accuracy has been quite modest.


Fig. 17. - Photos of the rad iometers employed by the Pr ince ton Group to conf i rm the P lanckian charac te r of the CBR in the 10-100 GHz region. The persons in the photo are David Wilkinson and his s tudents Robert Stokes and Paul Boynton. (Cour tesy by Paul Boynton.)

3{} B. MELCHIORRI and F. MELCHIORRI

Fig. 18. - Photos of the airborne experiment at 90 GHz carried out by the Princeton Group: the radiometer is calibrated immediately before the flight, while a liquid nitrogen source is employed in flight to check for the stability of the overall gain. (Courtesy by Paul Boynton.)

analysed by the groups involved in CBR study. Two atmospheric components dominate the millimetric region, H20 and 02. For very low water vapour content and/or high altitudes also 03 becomes important. Generally speaking, the absorption in dB/km due to the transition from a state i to a state j at a frequency v is described by

(17) ct(v) = C(P, T)F(v , vi-- vj) h ( v { - vy) exp -- kT --~ '

where C(P, T) is a func t ion of the p r e s su re P and of the t e m p e r a t u r e T. In the case of oxygen it tu rns out to be p ropor t iona l to PT -3, while in the case of wa t e r vapou r it is p ropor t iona l to the par t ia l p r e s su re of it, or to pT -2, p be ing the so-cal led absolute humidi ty , usual ly exp re s sed in g m -3. F is the so-cal led fo rm factor and descr ibes the l ine broadening . Various semi -empi r i ca l exp re s s ions have b e e n adopted for it: in the far in f ra red it s eems to follow quite well the Van-Vleck


Weisskopf approximation (Boltzmann distribution corrected for the effect of the radiation field)

(18) Fv~w = ~ + -- ~v~j (vii -- v-~ + Av 2 (v~j + v) 2 + Av ~ '

where vij = v.z -- vj and Av is the natural line width, proportional to the pressure and to T -~. It follows that oxygen emission is a rapid decreasing function of the pressure, while water vapour content plays a major role in the millimetric and submillimetric region. This point was not fully realized during the seventies, when the atmospheric emission below 3 mm was considered definitely too high to attempt ground-based observations.

On the basis of these considerations, since 1968 the group of Harwitt at Cornell initiated a rocket program to observe CBR near its Planckian peak, around I mm of wavelength. It was followed in 1970 by MIT with a similar experiment mounted on board of a stratospheric balloon. Both the experiments suffered of substantial problems, the Cornell experiments providing huge signals corrispond- ing to temperatures ranging from 3.4 to 8.3 K; MIT group had similar results during the first balloon flight. Schematic diagrams of these early balloon and rocket experiments are in fig. 19.

We believe that the failure of these earlier attempts had causes similar to those already analysed in the case of early radio attempts: lack of sensitivity, spurious signals entering via sidelobes and (specific for bolometers) leaks in filters in the near and middle infrared. A systematic comparison between InSb detectors (employed in early experiments) and Ge bolometers operating in a well-matched reflecting cavity have been carried out for the first time by the Florence Group [48] in collaboration with the Cornell Group, with the important conclusion that InSb is inadequate in sensitivity. Another systematic search on the properties of filters for far-IR applications was initiated by Baldecchi and Melchiorri [49-52] which finally led to the realization of interferential filters combined with Yoshinaga-type filters capable of a rejection factor larger than 106 outside the window of interest, and a transmittance larger than 50% in the window itself. A special'technique was invented to test high-rejection factors, by observing the transmittance outside the band as a function of the number of identical filters added along the line of sight.

The angular response of the detector was significantly improved by using parabolic Winston cone (Winston [56]) and by adding a set of diaphragms designed on the basis of the geometrical theory of diffraction.

The atmospheric problem, as already pointed out, requires a bit of caution. Figure 20 shows the absorption of the standard atmosphere at sea level. In the millimetric region the absorption is due mainly to three components: 02, Oa and H20 , water vapour being dominant in the frequency region beyond 300 GHz. While fig. 20 suggests that the windows around 2 and 3 mm are more transparent (and less emissive) than that around 1 ram, this fact depends on the water vapour content. In fig. 20 we have separated the oxygen and water vapour contributions: it is possible to see that for a water vapour content _< 0.5 ram H20 of precipitable water, the window around 1 mm becomes in fact more trasparent. It follows that one can have the same or even better chance of detecting CBR through the 1.2 mm window as the already tested 3 mm window.


b) removable 0.00025 cm Mylar membrane [ /-removable Mylar cover

_ )/2~-movable calibration outer cone. ~ ~ source

inner cone~/G.~, , 1 9 o ~ chopper

Mylar- ~ff ~ I / ~ g - ~ / / ~ / m o t o r [ / i l l /~/// k. ~ \ stainless

cold ~ ~ ' ~ ~s tee lDewar wlndow-~ ~ - ~ . [-t'/ rupture

a b s o r b e r ~ l ~ & ~ / ' ~ 2 It diaphragm I/ I ~ / ~ ' I ~ liquid He 1.5 K

He gas/" I [ ~ // ~_ .... [. ~_fi l terdisk efflux I / / / / / / / '~1 .sealed

Teflon lens [I?q( ~ / ~J--4\ copper can

collimating__j~L~\ / L_~J -stepup cone ~ COIl

In Sb heater detector \

chopper * thermometer

to reference I current source

filter ~ . ~

indium " ) ~ O-ring joint

|

,NN

c)

vacuum ~upper cone

cylinder C-.~ reference coil in~ / groove . ~ c h o p p e r blades ~ vacuu lT t - 'K~,\\\\\\\\\\\\

~lower cone

section superfluid He bath T=l.6 K

copper annulus

bolometer leads dihedral

mirrors

to constant current source and preamplifier

d)

window \ calibrator

~ ~ ] ~ 62 litre

I I \ I I l l lens-cone /"~ _- l \ ~#'N A ~ . . . . collimator ' I , : ~ , . , , ' ~ [ . . . . . . mirror

L / ~N" ~ " ~ 1 .... "-~ entrance , ~ ' ~ / / - ~ ~ ]- , "polarizer ] V I ' ~ _ ~ [_ ,cold [, A / t-K] ~ , blackbody |lens bolometer \ germanium

/ cone beam splitter polarizing

chopper

Fig. 19. - Schematic diagrams of four early ,,space~ experiments devoted to the study of CBR spectrum: the rocket instrument of Cornell Group (a ) ) recorded huge sky temperatures, apparently due to the presence of large instrumental sidelobes; a similar result was obtained by the balloon-borne radiometer of MIT (b)), corrected later on into more reasonable temperatures. The rocket instruments of BLAIR (Los Alamos) (c)) provided an upper limit to CBR temperature in the millimetric region consistent with a 2.7 K blackbody. Finally, the scheme is reported of the first Berkeley experiment (d ) ) which, however, failed during the first attempt. (Courtesy by K. Shivanandan.)

T H E C O S M I C B A C K G R O U N D R A D I A T I O N 33

I0 ~

10 4

103

"- / 2 10

o

~ 10 l

10 ~

1 0 - 1

10 -2 /

m m w i n d o w w a t e r v a p o u r ;

0 , 5 m m H20 i 2 m m i', : w i n d o w :', t, ii ," "

w i n d o w , : ~ :; ', ,' -~

0 200 400 600 v (GHz)

Fig. 20. - Atmospheric attenuation under very tow water vapour content. For less than 0.5 mm of precipitable water; the window at 1 mm becomes less emissive than the 3 mm window. On the basis of this consideration, Florence Group started in 1970 a systematic search for a very dry site, where to carry out observations of CBR spectrum in the millimetric window. This search finally led this group to set a very stringent upper limit of 2.7 K to CBR temperature between 1.2 and 1.4 mm: this was the first clear evidence in favour of a Pianckian shape.

In order to explore the properties of the atmosphere in the far infrared, the Florence Group in Italy initiated his work in 1970 and realized, in collaboration with the Laboratorio di Cosmogeofisica in Turin, an automatic radiometer operating in 1.0-1.4 mm atmospheric window at high mountain [53]. The scheme (see fig. 21 a), b) was similar to the Princeton radiometer, but a Ge bolometer was employed as a large band, large throughput detector. The radiometer was carried on the top of Testa Grigia Observatory on the Alps (3500 m a.s.l.). For the first time a sistematic study of the atmospheric emission was carried out along several months [54]. A first interesting resut of this work was the confirmation that the standard atmospheric model holds in the far infrared, and the excesses found by various authors were spurious. Finally, during a clear day and night on January 12, 1974 [55], it was possible to measure the sky emission with an atmospheric contribution of about i0 K corresponding to less than 0.3 mm of precipitable water. The radiometer was fully automatic and this allowed a sky scan, step by step, in a sequential way rapid enough (about 45 rain per scan) to have an almost stationary liquid-helium level in the reference source. The results of these exper iments may be summar ized as follows [55]: in the 1.2-1.4 m m atraospheric window the t empera tu re of CBR is <_ 2.7 K Since the possible systematic errors dominate this measurement , it is difficult to assess the statistical mean ing of this upper limit. If one assumes that the est imated ampli tude of possible systematic effects can be treated like a statistical error, then the upper limit is at 3a. Obviously, this assumpt ion is incor rec t and the upper limit found in the experi-


a)

Fig. 21. - Photo (a) ) and scheme (b)) of the 300 GHz bolometric radiometer employed by the Florence Group for measuring CBR through the atmospheric window at 1 ram.

ments has been e r roneous ly sometimes quoted as 2.4 K at 1~. What it really means is that the chance to have a value greater than 2.7 K is comparable to the case of 3G level, while CBR have equal probabili ty of having any t empera tu re below 2.7 K.

We have insisted in details about this expe r imen t not only because it was the first clearly demons t ra t ing the curvature of the CBR spec t rum across the Planckian peak, but also because i t was carr ied out after a long and detai led investigation of all the possible spurious effects. For these reasons we believe tha t the ag reement of the resul t with most r ecen t COBE m e a s u r e m e n t s is not fortu- itous. In 1975 the pe r fo rmances of the r ad iomete r have been tes ted th rough

THE COSMIC BACKGROUND RADIATION 3 5

a c o m p a r i s o n with the 90 GHz sys tem developed in Pr ince ton . An a t t empt to p e r f o r m s imul t aneous m e a s u r e m e n t s with the s ame r e f e r ence source f rom a dry site was ca r r i ed out in Nor th Norway, but failed due to the m a l f u n c t i o n of the rad iorece iver u n d e r the polar magne t i c field. Still this idea was la ter adopted by the so-cal led White Mounta in Collaborat ion.

We m a y conc lude tha t at the beg inn ing of 1974 it was c lear tha t CBR was decreas ing in power for f r equenc ies h igher t han 90 GHz; the p rec i se shape of the s p e c t r u m was far f rom being defined, however, especia l ly at the h ighes t f requen- cies. In fig. 22 we have s u m m a r i z e d the s i tuat ion in 1974.

...... 125 . . . . . .-- 3 . o K !

r . . . . . . . 2.8K . - / ,

0.5

2 . 0 K 2. 2 0 K 2 4 K . . . . . . . . . . . 2 ! K , 2 .oK, ......... , ......... . ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . '. . . . . . . . . . . . . . . . . . . . , . . . . . . . . . , . . . . . . . . . . . . . . . K ,

0.0 1 2 3 4 5 6 7 8 9 10 11 12 -1

a m

Fig. 22. - Some of the data on CBR spectrum available at the end of 1974: the four radio points are those of Princeton Group, while the upper lirait in the millimetric region is that of Florence Group. Two different representations of CBR spectrum are adopted in order to better indicate the meaning of the observations: the thick lines represent the best fit to the data.

3'3. Considerat ions on CBB spectrum. - A t the end of 1974 enough data were available to convince the scientif ic c o m m u n i t y tha t CBR is a real ex t raga lac- tic b a c k g r o u n d with a s p e c t r u m close to tha t of a 2.7 K blackbody. An inc reas ing n u m b e r of theore t ic ians s tar ted to be involved in the a t t empt of exp la in ing the origin of it.

CBR conta ins a huge a m o u n t of energy density. It is c u s t o m a r y in Cosmology to c o m p a r e the energy con ten t of any diffuse radia t ion with tha t of the mat te r , Pc " c2, whe re po is the cri t ical dens i ty of ba ryons = h 2 �9 2 �9 10 -~9 g cm - s and h = H / 1 0 0 k m s -1 M p c -1 iS the Hubble cons tan t no rmal i zed to the s tandard value of 100 k m / s / M p c , and c is often posed equal to 1. Therefore , following Car r [69], we in t roduce the quant i ty f J~(2) which is the ene rgy densi ty pe r uni t logar i thmic interval of f requency , normal ized to po �9 c 2. For ins tance , in the case of CBR we get

(19) ~'~CBR(,~m) = 2" 10 -~ h -2, Am = 1600 g m ,


fJr is related to the brightness 2I~ by the numerical relation

(20) Q = 2 . 1 0 ~ h_2[ ~I~ ] W/cm -2 s r - i �9

In fig. 23 (table II), we have compared f2CBR with that of several Galactic diffuse radiations, namely the star-light, the zodiacal light, the planetary dust emission and the interstellar dust emission. What is impressive from this figure is that CBR has an energy content comparable with that of the ,,local,, radiations, despite the fact that it is an extragalactic radiation. Another way to underline this point is the following: let us assume that the baryon density in the Universe is of the order of 10 -8o g cm -3, i.e. f]b ~- 0.05 as suggested by primordial nucleosynthesis; then, limiting our consideration to CBR photons, we have a photon-to-baryon ratio Fpb given by

(21) Fpb __ np 109 n b

What is the origin, the ultimate physical mechanism which produced such a huge amount of photons?

Several hypotheses have been suggested in the literature and we can class them into two cathegories, for the sake of simplicity: astrophysical models and cosmological models. In the first class fall all the models in which CBR is the result of an integration along the line of sight of the contributions from an appropriate set of celestial objects. The second class refers to the hypothesis that CBR originated at very early times, for instance via the annihilation between matter and antimatter, i.e. it originated when any celestial object was absent.

A certain bias was present, at least in the seventies, in the discussion about

10 -s

"~ 10-~ I I

10 .7

-8 lO

z~ CBR t

/ b a c k g r o u n d

\

1 I I I I

104 103 102 101 wavelength (gm)

Fig. 23. - Table II energy content of various cosmic and local backgrounds, measured in units of equivalent matter density (see text for an explanation). It is evident that the energy content of CBR is comparable with that of local backgrounds, despite the fact that its energy is diluted in the extragalactic enviroment.


TABLE II. - Energy density of primordial backgrounds. (adapted from B. J. Carr [69]).

Source Energy density far

Primeval Galaxies

Population IlI stars

Black Hole accretion in

a) galactic nuclei

b) pregalactic era

2 . 1 0 -7 (Z4 / 0 .2 ) -~ ( [1 +Zg]/IO)-I(~JO.1)(M/IO2M|176 -a) 4.10-6(1 +Z*/lO0)-l(~*/O.1)

10 -7 (1 + ZJ10)-I @/0.1)

7 " 10 -7 @/0.1)([1 + Z*]/IO) 1/a (f2J0.1) (M/10 6 M o) (T/IO 4 K)-a/a

Source 2 (peak) gin

Primeval Galaxies

Population III stars

Black Hole accretion in

a) galactic nuclei

b) pregalactic era

0,6 ([1 + Zg]/10) (M/102 M| -~ 4 (1 + Z*/lO0)

2 (1 + ZE/IO) @/0.1)-~/~ ([1 + Z*]/IO) 1/4 (~J0 .1)-~/4 (T/10 4 K) a/s

Symbols meaning:

Z~ metal yield for each star; Zg red-shift at which the stars generate a metaLlicity Z of 10 a. f2~ gas density. Z* red-shift of Population III burning; ~* stars density adequate to explain galactic halos.

efficiency with which accreting material generates radiation at red-shift ZE.

these two alternatives, because the first one was supported by the defenders of Steady State theory, in the hope of explaining CBR outside the Big Bang framework. We can review now the two models without such an emphasis, since Big Bang theory is almost universally accepted.

33.1. A s t r o p h y s i c a l m o d e l s f o r C B R . Several celestial objects have been considered as possible sources of integrated backgrounds (for a review of the subject see the article of Carr [69]). Among them we recall Primeval Galaxies, Population III stars, Blak Hole accretion (both at the centre of Active Galactic Nuclei and remnant of Very Massive Primordial Stars), Pregalactic Explosions, Decaying Particles.

The spectra of the diffuse backgrounds produced by these objects are shown in fig. 24. Two main considerations follow:

a) the spectra peak at the ,,wrong,, wavelength, namely in the near infrared or in the visible region;

b) for many of them the energy density is not enough to explain the CBR background.

In order to overcome the point a), one has to introduce a mechanism of frequency conversion, which shifts the peak wavelength toward larger values. A mechanism like that is well known in infrared astronomy, since it is operative in our Galaxy: it is represented by interstellar dust, which absorbs the star-light and

3 8 B. MELCHIORRI and F. MELCHIORRI

- 5 lO

10 -s

H

10 -7

, .~ckground

thermalization needed

10 -8

103 102 101 10 ~ 10 -1

wavelength (~tm)

Fig. 24. - Possible astrophysical sources of diffuse backgrounds: some of them (like active galactic nuclei (AGN), primeval galaxies, Jupiters, have not enough power to explain the presence of CBR). Others have comparable power but lie in a w r o n g wavelength region. They need to be thermalized, in order to convert their energy into radio emission.

r e -emi t s it in the far in f ra red (*). Cosmic dust has been the re fore hypothes ized, with an optical absorp t ion ~D and a dens i ty ~r~ D large enough to g u a r a n t e e tha t all the rad ia t ion emi t ted by the original source is abso rbed and re-emit ted . The p rocess is essent ia l ly governed by two equat ions

(22) s t ] , = (1 + Z , ) ~CBR,

(23) ~D = ~ , (1 + ZD) ~ >__ 1,

whe re the first equa t ion r ep resen t s the ene rgy ba lance , i .e . the ene rgy densi ty of

(*) The mechanism is usually referred to as ,r by dust,,; as a matter of fact, it is not a process in thermal equilibrium, since the radiation emitted by each grain propagates freely. However, the energy of optical photons is redistributed along the various degrees of freedom of each grain and in this sense a sort of equilibrium is attained, which allows us to describe the emission as that of a gray body, i.e. a blackbody multiplied by a wavelength-dependent emissivity.


the sources (given by their density f2, multiplied by the matter-to-energy conversion efficiency ~) equals the CBR energy at the red-shift of the sources Z,. The second equation gives the optical absorption of dust, which should be greater than one in order to convert efficiently the near-IR energy into far-IR radiation.

= n + 3/2 takes into account the deviation of dust emission from that of a pure blackbody: n usually ranges between i and 2. The results of primordial nucleosynthesis constrain the maximum value of f2, to be _< 0.2, while the lack of significant absorption toward quasars constrains QD <--10-4- Since ~D must be larger than one, we get

(24) (1 + Z. ) n+3/~ >_ ~"~D 1 .

If we assume a spectral power n----1 for dust, this condition requires

(25) ZD >> 25.

Obviously, Z, must be larger than this, in order to allow dust to absorb the radiation: if we put this constraint into eq. (20) together with the condition (by nucleosynthesis) that f2, < 0.2, we get

(26) e > 10 -2.

Very full sources fulfil this condition. For instance, our Sun has an efficiency ~sun ~- 7 �9 I0-4; very massive stars (i00 Msun) can reach 5 �9 i0-3 (Carr et al. [70]). Only accretion black holes have ~--~ 0.2

The conclusion is that we have a serious energy problem and one is forced to relax the constraints from primordial nucleosynthesis.

Even if we do this, another difficulty remains: as pointed out before, the dust emission differs substantially from that of a pure blackbody, especially at long wavelength. One is forced to introduce an ad hoc mechanism of thermalization. The simplest way, namely the presence of a huge dust density to make the Universe opaque, is forbidden by the observed transparency up to Z-~ 4-5. Therefore, we have to hypothesize the presence of exotic grains, being very efficient emitters at long wavelenghts. Several centimeters long whiskers have been suggested, although their existence in the hostile extragalactic environment is doubtful [71, 72].

In conclusion, two main difficulties make the astrophysical origin of CBR umpalatable: the energy content of CBR is such that only the conversion into energy of a huge amount of matter can satisfy it. The requirement is such that one is forced to violate the upper limits posed by primordial nucleosynthesis to the total baryonic matter content. Secondly, the blackbody spectrum can be recovered only if an appropriate mechanism of thermalization is assumed: the transparency of the Universe requires that such a mechanism is not based on a high dust density. Very long exotic grains must be hypothesized in order to get the needed emissivity.

The above difficulties have made cosmologists skeptical about the possibility of explaining the entire CBR emission via astrophysical mechanisms. On the other hand, it is undisputable that at least some of these mechanisms are in fact


operative: if a certain amount of cosmic dust exists, it will contribute to the far- infrared background, thereby distorting the pure Planckian spectrum of CBR; therefore we will reconsider them in the framework of the possible causes of CBR distortion.

3"3.2. C o s m o l o g i c a l m o d e l s . It s very easy to produce a huge amount of radiation and a large photon-to-baryon ratio via matter-antimatter annihilation. Also this mechanism has serious drawbacks, however, at least in its more naive version.

Let us start with a symmetric Universe, made by the same amount of matter and antimatter. At temperatures large enough (say 1 GeV) the equilibrium between nucleons and antinucleons of a given mass ~r~o/~b VS. photon is determined by the annihilation rate equation

~Tb/ab m ab (27) Nphotons oc - - exp [-- mb/ab/T],

where the index b or ab means baryons and antibaryons; see, for instance [73]. As the temperature of the Universe cools down the equilibrium is mantained and more and more photons are produced via annihilation; at a temperature of the order of 20 MeV the residual density of matter and antimatter is so small that the annihilation rate becomes much smaller than the expansion rate of the Universe. Therefore, the two densities of matter and antimatter are frozen in. Practically, it means that the density is so small that the probability of any residual annihilation is also small within the entire life of the Universe. By inserting T = 20 MeV in eq. (25), we get

Nb/~b ,,~ 10 - 18

( 2 8 ) Nphotons

a number which is too small with respect to the observed of about 10 -9. This is the first difficulty of this simple scheme: we get an overproduction of photons. Moreover, another fundamental difficulty is represented by the fact that astronomers have been unable to find any evidence of antimatter in the present Universe.

A possible solution to both these problems consists in hypothesizing a ,,segregation mechanism,, which should have operate well before T = 20 MeV, in order to both separate matter from anti-matter and frozen in the photon-to-baryon density at the observed value. This would be a very a d h o c mechanism and non-convincing physical reasons for it have been proposed.

A rather different and revolutionary approach is that suggested by Sacharov[74] in 1967. He has added three new hypotheses:

i) in the early Universe baryon non-conserving interactions occurred;

ii) we have also charge-conjugation and charge-conjugation plus parity violations (C and C P violations);

iii) both i) and ii) occurred during a departure from the thermal equilibrium.


These three hypotheses are what we need for having a process of non-symmetric baryon and antibaryon decay which finally led to a small amount of baryons, complete cancellation of antibaryons and a photon excess comparable with that observed.

One should stress that the matter-antimatter annihilation plays a secondary role in this process: it is the matter and antimatter decay which determines the final ratio and in order for it to be relevant the annihilation should have to play a minor role, i.e. the annihilation is used to cancel out the antibaryons after the asymmetry has been estabilished. It can be shown and it is intuitively understand- able that the presence of thermal equilibrium would lead annihilation to restore the symmetry in the baryon and antibaryon densities, a fact which explains the third requirement iii).

The basic scenario for baryogenesis has been illustrated by several authors {75-80]. For a recent review of the subject, see [73].

One starts by hypothesizing the existence of a superheavy boson (mb >--- 10 '4) whose interaction violate the baryon conservation. The precise nature of this X-boson is unknown; it could be the Higgs boson predicted by GUT. It is easy to show how the system goes out of equilibrium. As the temperature of the Universe T becomes smaller than m b ( remember that in our units k = 1 and c = 1) the equilibrium between X- and anti-X-bosons is governed by their decay rate Fa vs. the cosmic expansion H (annihilation is negligible under these conditions). We assume Fd -- H so that the system rapidly goes out of thermal equilibrium.

It is easy to understand the necessity for condition ii) by considering the fact that if we do not introduce a preferred arrow in the decay process both final baryon excesses and antibaryon excesses are equally plausible and the net result would be again a symmetric Universe in which a segregation mechanism is required. To illustrate better this point let us hypothesize that the early Universe is composed by some kind of particle X and antiparticle X~ and both decay in two channels with baryon numbers B: and B2 and branching ratios r and (1 -- r) (and the corresponding quantities for the antibaryons). The two decay equations are

(29) B~ = rB~ + (1 -- r ) B z ,

(30) B ~ = - r a t d , -- (1 -- r a ) B z .

By combining the two equations we get for the residual baryon excess

(31) Boxcess = B~ + Bzo = ( r - - r , , ) ( B , - - B.~) .

In this equation the quantity B~ --B2 expresses the baryon non-conservation, while the quantity r -- r a represents the preferred arrow and it is related to C and CP violation.

In conclusion, the Sacharov model provides a final baryon-to-photon ratio

Np ' '

where F is an appropriate function of the decay rate Fd v e r s u s the expansion rate H and of the C and CP violation efficency a. One would expect a GUT providing

42 B. MBLCIIIORRI and F. MELCIIIORRI

a precise prediction of the baryon-to-photon ratio: unfortunately, C and CP violations are not incorporated in GUT and e remains a not well-defined quantity. For a detailed discussion of this point, see, for instance [73].

We can say, in conclusion, that the Sacharov idea can explain qualitatively the observed matter, antimatter asymmetry in our Universe as well as the photon-to-baryon excess; a detailed quantitative estimation is waiting for a theory of the C and CP violation in the superheavy-boson system.

At present, the origin of CBR is attributed to the above-discussed cosmic mechanism, although one cannot exclude that astrophysical mechanisms could have, at least partially, contributed to it.

34. The search for ,spectral distortions: theoretical expectations. - We have already reported earlier CBR observations. The demarcation between these measurements and the new generation of space instruments may be located around the end of 1973, when Sunyaev [60] presented at IAU Symposium No. 63 a paper describing the behaviour of a mixture of a hot ionized gas and photons when some sort of energy injection occurs. This paper opened the way to the study of the so-called intrinsic CBR distorsion, i.e. deviations from the pure blackbody spectrum due to the interaction of CBR photons with ionized matter. This problem had been in part raised by Weymann [103] since 1966: he observed that CBR could interact with the ionized hydrogen predicted by the Gunn-Peterson test(*), thereby giving rise to a spectral distortion.

For a theoretician the question is intriguing: one should write down the Boltzmann transport equation in curved space-times with a source term containing the contribute of bremsstrahlung (photon creation by electron-proton collision), Compton scattering (energy exchange between photons and electrons) and double Compton scattering (as above but with creation of photon pairs). For a formal analysis the reader is invited to refer to the work of Bond [63]. In the case of CBR plus primordial plasma the situation is rather peculiar, as pointed out by Zel'dovich(**): bremsstrahlung is negligible, electron-proton collisions being much less frequent than photon-electron interactions (remember that the photon density is some 9 orders of magnitude higher than proton density!). Therefore, if for a while we disregard photon creation, the Bolt,zmann equation reduces to the so-called Kompaneets equation [66]:

(33) Compt- " 7"e c2 e x k + X + X 2 ,

where n is the photon occupation number given by n = (c3/2hv 3) I v and I v is the spectral brightness.

The solution of this equation has been analysed by Sunyaev [60]. tqrst of all, if there is time enough, the injected energy will be redistributed until a new

(*) The so-called GP test consists in the lack of absorption in the light of distant quasars for Lyman e photons; the recently discovered Lyman e clouds indicate that only 10- s of hydrogen is neutral and confirm the validity of the test. (**) The precise comment of Zel'dovich to Sunyaev paper was ,CBR is like a 100 year old virgin-being virgin just because nobody wished to violate herb, [60].


equilibrium is reached: this corresponds to the case ( S n / S t ) = 0 in eq. (31). The solution is known as Bose-Einstein spectrum:

2hv 3 1 - dv (34) I , dv c ~ exp [hv / kT + It] -- 1 '

where the quantity It is the chemical potential: roughly speaking, the blackbody spectrum is not recovered because the total number of photons is unchanged, while the radiation energy density was increased by the energy injection. The chemical potential measures this excess of radiation energy ApT , namely

(35) Ap~ " ~ w T 4 exp [It/kT] ,

where w is the Stephan constant. The spectral distortion due to eq. (34) is negligible for large v, i.e. when

hv/kT>> #, while in the long-wavelength region it produces a paucity of photons with respect to the blackbody at the same temperature. More recently, Hu and Silk [93] have suggested that It could be negative if the injected energy contains a substantial number of photons: in such a case it is possible to restore the Planckian spectrum by re-arranging the injected photons.

This situation holds in the red-shift region l0 s < Z_< 103. For larger red-shift bremsstrahlung and double Compton have time enough to provide the needed photons and every energy injection is thermalized into a blackbody with a sligthly higher temperature.

In any case, one has to take into account the effects of bremstrahlung and double Compton even if they are not enough to restore the blackbody spectrum: this analysis has been carried out by many authors [94-96]: the qualitative result is the following. The injection of energy has the initial effect of rising the temperature of the electrons: Compton scattering shifts low-frequency photons toward higher frequencies, so that a deficiency of photons is produced in the RJ part of the spectrum. Bremsstrahlung and double Compton tend to compensate such a deficiency and the final effect at recombination is that of a small decrease in CBR temperature around (hv/kT) ~- 10 -2. Hu and Silk [93] have pointed out that the residual distortion is rather sensitive to the baryon density, thereby offering an alternative to the classical methods for estimating the mean density of the Universe.

For Z smaller than 10 3, there is no time to redistribute energy up to the Bose-Einstein equilibrium. The resulting non-equilibrium spectrum is governed by the Comptonizat ion parame te r g, given by

Z

f k(To- (36) g = - �9 ~rrr/~ cdz ' ,

m e Cz o

where T e is the electron's temperature, T~ is the photon's temperature, aT is the Compton cross-section. The final result is a general shift of the photon's frequencies toward higher values, while the number of photons is obviously unchanged.


By using y it is possible to simplify Kompaneets equation to

(37) ~ y - x -~x x ~ x ]

the solution of which is, for small deviations from the blackbody,

I exp [x] + 1 ] (38) Air -- x y exp [x] x 4 . I v exp [x] -- 1 exp [x] -- 1

In the Rayleigh-Jeans limit it takes the very simple form

( 3 9 ) A T ~ ~ - - 2 g .

T

This means that photons are removed from the RJ region toward Wien region, where the change in temperature is

ATw (40) - - ~- x g .

T

This basic idealized picture has been rediscussed by several authors [57-59, 62, 64, 65] by adding many details, but the results did not change substantially. The entire matter has been recently re-analysed in two eccellent papers by Salati [61] and Silk [67] and we suggest the interested reader to refer to these articles.

In our opinion the widely celebrated paper of Sunyaev [60] contains two basic pieces of information:

i) We cannot explore the energy story of the Universe for Z_> l0 s, because every energy injection had time to be thermalized. This practically means that all the most energetic processes, from the nucleosynthesis to inflation lie outside our possibility of investigation. From Z = l0 s down to Z-- i000 the only unavoidable process expected to release some energy is that of galaxy formation. The exact amount of energy dissipated into the radiation field depends on the details of the theory and on the spectral index of the perturbations. For a rough estimate we may use the formula

(41) i t - ~ 3106 [ ~ ] 2

and values of # as small as ~- 10-4-10 -5 are expected. Therefore, we may conclude as a first result of Sunyaev analysis that primor-

dial Universe is perhaps too quiet to produce significant deviations from the Planckian shape of CBR. A detection of # >> 10 -4 would be rather surprising. On the other hand, a measurement of # at the level predicted by theories of galaxy formation would reinforce the internal consistency of our view, but the values anticipated by the theories are well below the present accuracy of the observations.


ii) The second important piece of information refers to the rather high sensitivity of the shape of the CBR spectrum to the status of the intergalactic matter after recombination has occurred, i.e. for Z < 1000. This point has been raised when X-ray astronomers attempted to explain the 2-50 keV photon background [651 as due to free-free emission by a hot intergalactic medium.

Let us assume that for some reason the intergalactic medium is ionized and it can be described by a plasma with a thermodynamic temperature T A cont inuum energy transfer will occur between electrons and CBR photons, via Compton scattering. The rate of energy transfer is

4kT (42) AF-,n~- c2 C~TneWT4~,

m e

where w is the Stephan constant. The time scale for this process is of the order of ( ( 3 / 2 n k T ) / A E ) ) << Hubble

time. Therefore, the process is very rapid and the energy injection into CBR is substantial. Equation (40) provides the way to estimate y (or an upper limit to it), while we may relate g to the temperature of the intergalactic gas via

(43) y = 4 �9 10-8(1 +ZS/2Ts ,

where Zi is the red-shift at which reionization occurred and T5 is the temperature of the gas in units of 105 [68]. It follows that observations can constrain the temperature of the intergalactic medium: but measurements of CBR spectrum cannot decide i f IGM is ionized or not: they may only set an upper limit to the plasma temperature. To get a definite answer to this problem, one has to analyse the behaviour of the ionization fraction X. If the ionization is produced by an equilibrum between collisional excitation and recombination, the minimum temperature required to ionize the IGM in such a way to pass the Ounn-Peterson test is of the order of

rGunn-Pet . . . . . ~___ 2 " 105 .

If some re-ionizing mechanism is at work, the temperature could be as low as 104 K. Therefore an ionized IGM could exist with g < 10 -6, well below any reasonable observational possibility.

We conclude that the point ii) of Sunyaev paper allows the observers to decide if a hot ionized gas exists (and therefore if the X-ray background is due to it), but the minimum temperature required to ionize the gas is too small to produce detectable effects on g. This last point leaves open the possibility that the recombination never occurred and the Universe remained ionized: although this fact has no observable consequences on the spectrum of CBR, it would blur the spatial distribution of CBR, thereby limiting our possibility of observing primordial anisotropies. A summary of the possible spectral distorsions is shown in fig. 25.

What we have described up to now are called intrinsic CBR distorsions in the sense that they are due to the interaction between CBR and matter.

In the previous paragraph we have outlined that several other backgrounds due to extragalactic sources can sum on CBR thereby producing an apparent distortion


300 cm 0.02

a)

0.01

o ~ o . o o

-0.01

-0 .02 3.5

3.0

~ 2.5

30 cm 3 cm 3 m m 300

\..

. . . . . . . . ~ . . . . . . . . , . . . . . . . . , . . .

. . . . \ . . . . , . . . . . . . . , . . . . . . . . , . ,

\ x

J

2.0

1.5 10 -1

10 -10

10 -11

10 -12

\ \

\ J

10 0

I J

b)

I

100

f J f

. . . . . . I , , , , , , , , I

101 102

frequency (GHz)

i I

W l "

2.7K

i I I , I

300 ' 500 I I I 700 960 wave length (pro)

10 3

s

TABLE I I I . - Stars and dust parameters for the six models. z T(K) z~ 1015 no cm-3 Label

100 1.4" 105 100 0.003 a 40 0.6" 105 40 0.005 b

100 1.4' 105 10 0.1 c 40 0.6" 105 10 0.1 d

100 1.4' 105 2 1 e 40 0.6.105 2 1 f

Fig. 25. - a) Expected spectral distortions of CBR due to Compton scattering with hot electrons, injection of photons produced by free-free mechanism and early energy injection ((AE/E) ~ i0-2) producing a Bose-Einstein spectrum -- Planck, -.. Compton y, -- - Bose-Einstein, ------ free-free. The distortions are represented in terms of brightness (upper panel) and temperature (lower panel): it follows that measurements in the millimetric region thereby constrain Compton distortions, while radio measurements are more efficient in setting upper limits to energy injections toward Bose-Einstein spectrum. (Adapted from A. Kogut, preprint 1993). b) Expected spectral distortions produced by dust re-radiating the energy emitted by a Population Ill of stars with typical temperatures as given in table II (adapted from [85]) and table Ill.


on its spectrum. The analysis of these possibilities has been stimulated by early spurious results wich suggested the presence of submillimetric excesses.

The possiblity of extragalactic dust emission and the amount of radiation expected for the various types of grains (graphite, silicate, iron, ice) has been investigated since 1978 by[84]. The first serious attempt to explain observed distortions of CBR spectrum in terms of dust grains having reasonable physical properties was that of Aiello et at. [81, 82], followed by many other papers. At about the same time Rowan-Robinson proposed a similar approach [83]. Despite the fact that the final spectrum will strongly depend on the absorption efficiency of the dust, the general scheme of the process is quite simple: a generation of pregalactic stars (Population III?) is assumed to be surrounded by dust, which absorbs the UV and visible radiation of stars and re-emits it in the infrared. Things go on like in the case discussed in the paragraph dedicated to the astrophysical models of CBR, but now the energy requirements are less stringent, because we do not want to produce the entire CBR spectrum but a tiny deviation from it. For instance, Silk [117, 67] has shown that a reasonable choice of the parameters can easily produce a one-per-cent level of distortion. The general model of dust distortions does not require that the energy source be stars, however; Fukugita [118] has considered the possibility of decaying particles producing an UV excess, which Adams and McDowell [119] employed in their distortions model as a source for dust heating. The main results of this analysis are the following: a near-IR background is expected, as due to the star-light not thermalized by dust: a far-IR background is emitted by dust and contributes to the distortion of CBR. The ratio between near-IR and far-IR fluxes depends critically on the optical depth of star-light through cosmic dust. Assuming a uniform distribution of a galacticlike dust with a density n = no (1 + Z) a, we have [85] for the optical depth

ZF

0

where a is the grain radius, of the order of 10-5 cm; Qabs i8 the grain absorption coefficient; ZF the red-shift of grain formation. In order to calculate the fir background generated by dust, de Bernardis et al. [85], have numerically integrated the transport equation:

5 i s 3& [v ( t ) , t] I s [v ( t ) , t] e~ I s [v ( t ) , t] (45) St a

~I z) 3& (46) - - ~ [v ( t ) , t] = -- - - I s [v ( t ) , t] -- ot~I D [v ( t ) , t] + c J D Iv ( t ) , t]

a

where a is the scale factor of the Universe; I s is the near-IR background; I u is the far-IR background; c% = crt( a 2 } Qau~(v)n(t) is the dust absorption coefficient; jD = [~ ( a S } Qabs (~)] n ( t ) B v [Td (t)] is the source term produced by heated dust; B [T d (t)] is the blackbody brightness per unit frequency interwal. The dust


temperature Td may be evaluated through the equilibrium between absorbed and emitted power:

f (47) f Qabs(V)B v [Td (t)] dv = Qabs(V) I[v(t), t] dv.

0 0

In fig. 25b) there are shown the expected backgrounds produced by various combinations of star-light (determined by stars temperature T) and dust density, as indicate in table III. It follows that measurements of CBR distortions in the millimetric region would provide information (or upper limits) on cosmic-dust density as well as primordial dust temperatures.

3"5. Experimental techniques for searching CBR spectral distortions.- Three techniques have been proposed in the literature: the first one is based on improvements of the early absolute measurements. The second technique has been proposed by Rome Group [88] and consists in an application of the so-called dipole anisotropy. Finally, Rome Group [120, 121] proposed to search for CBR noise, i.e. both quantum and wave noise in the radiation field.

3'5.1. Ab s o 1 u t e r a d i o m e t r y o f C B R. In the radio region the measure- mens of CBR spectrum proceeded slowly: since 1979 for more than ten years Berkeley group, in collaboration with Milan and Padua, have improved their observations at 50, 36, 21, 12, 7.9, 6.3, 4.0, 3.0 and 0.9 cm of wavelength. The most important feature of this long and expensive work was the use (where possible) of a common reference source, consisting in a huge He dewar in which a microwave absorber was immersed. Despite this significant effort, the results have provided a little improvement in the previous accuracy. The weighted average of all CBR measurements yields

(48) TCBR = (2.74 + 0.01)K; )~2 = 37 for 40 d.o.f.

In fig. 26 they are plotted togheter with previous radio measurements. The most striking feature is represented by a significant deviation from the mean temperature around 1.41 GHz, Kogut et. al. [97].

Much more impressive was the progress in the submillimetric region. Starting from 1975, the early broad-band bolometric observations have been changed into spectrometric observations, thanks to the invention by Martin and Pullett [98] of what is known as the polarizing Michelson interferometer. Several groups attem- ped to adapt such an instrument for CBR observations, namely Richards in Berkeley[99], Gush [100] in Vancouver, Beckmann and Robson [101] in London, while Marsden [102] in Leeds employed a lamellar grating interferometer. First of all, the cavity where the bolometer was located was usually too small with respect to the observed wavelengths to be considered a blackbody. The resulting cavity modes made the calibration of the system troublesome: see fig. 27. This question was settled, by the careful analysis of Baltes and Stettler [106] of the modes of a finite cavity. A second problem was represented by t he residual atmospheric


4.0

3.5

3.0

2.5

2.0

I I I I I I I I I I I I I IILII I I I I I I I I I I I I

r

for reionization ]i

ii ,

1.5 I ! ] I IIL]1 I I ] L IIIIL ] q ] I ]LIb] L I I ] ] ] ] b ] 10 -I i 0 ~ 101 10 2 10 3

f r equency (GHz)

Fig. 26. - Some of the most recent spectral measurements of CBR: continuous bars refer to White Mountain results, dotted bars are from old Princeton data: COBE-FIRAS results are indicated as a shaded box, the dashed line is for reionization, the continuous line for Bose-Einstein distortion. Note that in the radio region free-free emission would lead to a change in the sign of the dipole anisotropy.

emission present at balloon altitude. Richards [99] was able to show that the already available atmospheric models are adequate to fit and subtract the atmospheric emission, when the theoretical and observed spectra are normalized at the peaks of the most prominent lines, as shown in fig. 28.

All these experiments produced spectra which, after atmospheric subtraction, were in substantial agreement with a 2.7 K blackbody. The experiment of Queen Mary College Group [107] has ben criticized by Berkeley Group, being the reported atmospheric emission rather different from that predicted by the theory and observed by Berkeley experiment [99]: see fig. 29 for comparison.

The small deviations from the Planckian spectrum found by Berkeley group in this and subsequent flights are now considered as spurious. The origin of them has been identified by Richards as due to radiation scattered and /o r emitted by the collecting horn, which was outside the geometrical field of view, but still contributed to the modes of the accepted radiation [108].

A significant improvement in absolute measurements was suggestd by Mar- tin [109] by using an on-board reference blackbody the temperature of which can be continuously varied between 2.0 K and 3.5 K: in this way, the bolometer is used as null-detector thereby reducing the uncertainties in calibration, i .e. the errors due to calibration are affecting the distortions only, while a zero signal is expected if the spectrum of CBR and that of the reference blackbody are identical. Later on,


.~10-'

Q &

~!~ ~!1~'~ ' ~ ~ ~ " ~ cavity modes

I000 1 bolometer iJ

cavity r~ W = - - cavity le

10 101 10 2

cavity length

wavelength

Fig. 27. - A bolometer inside a cavity [99] is not a good fiat absorber, if the dimensions of the cavity are comparable with the wavelength of the observed radiation, like in the case of CBR. Cavity modes complicate the spectral response of a bolometer making it difficult to realize a precise photometric calibration. Theoretical computations from [106].

this technique has been employed by COBE, while a proposal presented by European groups (CIRBS) was refused by ESA.

The CBR spectrum obtained by COBE-FIRAS is shown in fig. 30, together with the similar spectrum obtained by Gush at about the same time. The two instruments employed in these experiments are shown in fig. 31. To date these measurements appear to be the most accurate determination of the CBR spectrum in the millimetric and submillimetric region. It is disappointing for an experimen-


measured sky spectrum at balloon altitude 1976

covolution

lmm 0.5 mm measured spectral

1 m m

theoretical atmospheric emission

X

o

CBR spectrum =

1 mm 0.5 mm

Fig. 28. - The measured sky emission at balloon altitude is dominated by atmospheric emission. This however is stable enough to allow a renormalization of the data to the peaks of the most intense lines. It is possible to recover the CBR spectrum by subtracting the theoretical atmospheric spectrum (normalized as above) from the data, as shown in this set of data provided by Berkeley group.

tal physicist to note that so important results have not been supported by detailed information on the performances of the instrument. At first glance the zero-system employed by COBE Team looks very simple and convincing. One should keep in mind, however, that interferometers are very peculiar instruments.

The signal output of an interferometer, when the path difference is Ax is given by

oo

(49) W ( x ) = -~ u a ~ S ( v ) 1 + cos 4 u v x 1 ~ dr ,


5

4

T 3

~ 2

' o 0 •

'~ 30

�9 '~ 20

10

I I I 0 10 20 30 40

frequency (cm -1)

Fig. 29. - The spectrum recorded by Queen Mary College Group [107] turned out to be about six times less intense than that later on measured by Berkeley Group and with a rather different shape. A degraded instrumental resolution may explain the effect, at least partially. In the lower part of the figure we have quoted the exptected spectrum on the basis of Berkeley results. (Adapted from [102]).

whe re S(v ) is the source br igh tness and f2 is the solid angle of the optics. Pract ical ly, this m e a n s tha t a finite field of view has the effect to shift the f r equenc ies of the i ncoming radia t ion by an a m o u n t v (O/4~z). In the case of FIRAS one min imizes the d i f ference be tween the power rad ia ted by the sky, let us say BB (v), and tha t rad ia ted by an on-board re fe rence , BS(v) .

The previous equa t ion the re fo re has to be rewr i t ten as

(50) I iIBB [ [ (Qs')ll7 W ( x ) = ~ rca 2 (v) 1 + c o s 4rcvx 1 - - ~ -

0

[, _,_ F,,x (, _ Oro< d,, 4 ~ / J J '

where we have a s s u m e d tha t the solid angle in the two cases m a y be slightly different. Under these c i r c u m s t a n c e s it is not c lear at all tha t W(x) = 0 implies


L

2.90 - -

2,80

-~ 2.70 - -

~D c~

2 5 0 -

10 -2

I I l i l l I

t I I I I I l l

10 -1

, i ' ' ' " 1 , L t , ; , l l i , i _ _ _

i, ~ -~r ... ,~.~

m

r i , ; l l l l l I i l ilill i l~ 100 101

frequency (cm -1)

Fig. 30. - Some of the most recent measurements of CBR spectrum: the dotted line represents COBRA results with the uncertainty shown by the bar at the left of the curve. Triangles refer to interstellar molecules measurements, while the squares are from White Mountain collaboration. The diamond corresponds to the balloon-borne experiment of Princeton Group.

BB (v) = BS@). Compton distortion, which is propor t ional to v in the Wien region, may be masked by this spur ious effect!

The lack of considera t ions about this and o ther impor tan t effects suggest to cons ider FIRAS results with a bit of caution. If we forget these problems, the most accura te spec t rum is that obta ined in 100 minutes of observat ion toward a region of low dust content , the so-called Baade Hole (1, b ) = (143 ~ 53 ~ (see fig. 32)[113]: the spec t rum is that of a blackbody with

T - - 2.735 -t- 0 .060.

The data exc lude any spectral deviation larger than 0.25% of the peak brightness. When this cons t ra in t is inser ted into the formulae for Bose-Einste in spectrum, it gives an uppe r l imit of chemica l potent ia l tt <_ 2 �9 10 -3 (95% confidence level). A m u c h bet te r uppe r l imit is posed to the Comptoniza t ion pa ramete r , the Compton effect being more efficient in the mil l imetr ic region, g < 2.5 �9 10 -4 (95% c.1.).

The resul t obta ined by the COBRA rocket e x p e r i m e n t of Gush [114] are in agreement with those of FIRAS with a small improvement in the t empera tu re accuracy

T = (2.736 __ 0.017) K


sky

r,~t'erence mkbody

~ / m o v a b l e sky [I I \\ mirror \ I',/ ',

bolometers

referenc msplitter ', ', input ~ _2~-----'~/ "-4 ~ ~ k ' ~ ', ~.lo~h.a.~ ~ 7 - - ~ / ~ / I ~ I\\ movable', ~. . b e a m s p l i t t e r . ~ ,

l l ~ a'rr~ T < "~"" iI . i i ' . i > m = 2K ,' -.."" "'-.,." ... -- ," ovable I

(~ / ~ I . . . . . . . "-~ mirror, bolometers | " - . - |

| bolometers A . . . . . . . . . .A. . . . . : t . J . . . . ~ . . . . . . . . . . :

Fig. 31. - Optic diagram of the two most precise radiometers employed in the measurements of CBR spectrum left: FIRAS-COBE; right: COBRA. In both cases a differential arrangement has been selected which compares the sky radiation with that of a blackbody at variable temperature. A polarizing interferometer is employed to search for spectra distortions.

._. 1.0- 7

~ 0.8,

"~ 0 .6 .

~ 0 .4

0.2-

0 10 20 30 40 50 60 70 80 frequency (cycles/cm)

Fig. 32. - Measurements of CBR spectrum carried out toward the Baade Hole, a region free from galactic dust. The points are fitted with a blackbody at T = 2.735 K and the uncertainty is of 60 inK. (Provided by COBE team).


with no deviation from blackbody spectrum in the 3-16 cm -1 spectral region within 0.3% of the peak (__ 10 mK).

3'5.2. T h e d i p o l e a n i s o t r o p y . Since 1907, Mosengheil[89] had noted that an observer moving at speed v with respect to the walls of a blackbody would observe a spectrum with a slightly different temperature, given by

1 (51) To~ = Ts r~2-1/2 [1 + f l cosO*] ,

(1 P )

where fl = (v /c) , O* is the angle between the direction of observation and that of motion, as measured in the rest frame of the blackbody wall.

In the case the angle is measured by the observer, one has to take into account the effect of aberration, so that

(52) cos O = cos O* + ,6

1 + flcos O*'

The equation becomes

(53) Tobs= T~ [ 1 , 6 2 + ] y[l + f icosO]~- T~ l + f l c~ + f l 2 c ~ . . . .

At first order this relation represents what is called dipole anisotropy. One can re-express the above formula in terms of brightness, instead of temperature. To this purpose Bottani et al. [90] have introduced the spectral index o~ (v) = (v/Iv)(8I~/8v) and we get

1 f12 ] . (54) /robs (robs) = Is (Vob~) 1 + ~ (3 -- ~) + (3 -- a) fi COS O + O (fi2~2)

In the case of a blackbody

x exp Ix] hv (55) c~ = 3 -- " x - .

exp [x] -- 1' kT

The existence of a dipole anisotropy in the spatial distribution of CBR has been predicted by Sciama since 1967 [36, 104]: he pointed out that a measurement of the motion of our Galaxy with respect to the last scattering surface would result in an important cosmological toot, when compared with the optical observations of the motion with respect to other galaxies and, expecially, the Virgo Cluster. On the other hand, Sciama did not discuss the sky pattern of the dipole anisotropy, limiting his considerations to the maximum amplitude, when the observations are along the line of motion.

Peebles and Wilkinson [105] were the first to point out the cosine distribution of the dipole anisotropy; they re-derived the Mosengheil formulae independently.


The search for CBR dipole anisotropy started in 1968 with the so-called YUMA experiment, carried out by Princeton group in Arizona [110]. It provided a value of (1.1 _ 1.5) inK, a limit improved by Beery, see Partridge [111] down to 0.7 _+ 1.2 mK.

Unfortunately, these erroneous results were in agreement with the arguments of Tamman [112] in favour of a very low peculiar velocity of our Galaxy with respect to Virgo Cluster, believed to be at rest with respect to the last scattering surface. Therefore, they contributed to make the scientific community skeptical v s . the detection of CBR dipole anisotropy reported by Conklin [91] in 1969.

The dipole anisotropy was observed for the first time by Conklin [91, 115] from ground and by Henry [92] at balloon altitude. Conklin detected an equatorial component of 1.9 _+ 0.8 mK directed toward 10 h of right ascension, while Henry measured 3.3 ___ 1.2 mK toward 14 _+ 23 hours of RA and -- 20 ~ _ 20 ~ of declina- tion.

Since COBE has provided both the spectrum and the direction of dipole anisotropy with an unsurpassed accuracy, we may be interested in comparing them with early measurements. At the beginning of the eighties four groups have been involved in the search for CBR dipole anisotropy, namely Princeton, Ber- keley, Florence and MIT. The directions quoted in early papers are represented in fig. 33 and the amplitudes in fig. 34, where also COBE results are reported for comparison.

It is clear from these figures that Conklin and Henry observations were inconclusive, although not far from the final result. Among the three groups involved in these measurements, Princeton and Florence provided observations in agreement with COBE data, within the experimental errors. On the contrary, Berkeley group and MIT indicated directions which are wrong well outside the experimental uncertainties. The typical signals produced by the dipole anisotropy

6-

5 ~

4-

~ 3 -

2-

1-

Pr ince ton 80

\ Florence 80 [i . ~ Berkeley 79 ~

10

Fig. 33. - Early data of Princeton, Berkeley and Florence groups on dipole anisotropy amplitude compared with COBE-FIRAS result (thin horizontal line): previous old data by Princeton [67] and Conklin [72] suggested a lower value.

I I I I I I I I I I I I 0 20 30 40 50 60 70 80 90 100 2 3 400

frequency (GHz)


20 -1 ~2 rkefey

9 10 11 12 13 14 15 16 17

Fig. 34. - As in fig. 33, but for the direction of dipole anisotropy. Florence and Princeton results are consistent with COBE data, while Berkeley [79] and all MIT results indicate values outside two standard deviations.

in the far-infrared channel of Florence radiometer are shown in fig. 35. This signal indicates the substantial progress obtained during the ten years separating these observations from those of Henry. In 1989 Florence results have been confirmed for the first time by Richards group [135]. The main difference between Florence and Berkeley experiments was in the choice of a double-beam system (Florence) where two sky regions 6 degrees apart were confronted, and a single-beam system (Berkeley) where the sky was compared with an on-board reference source. This last solution was employed by MIT group in a new, multifrequency experiment [136]. Figure 36 shows the results of this last experiment: the comparison with the expected dipole signal indicates the presence of a huge offset in the data, although the direction is consistent with COBE. Such a large offset is in our opinion the result of the choice of a single beam and, with its fluctuations, it could be responsible for unkown signals recorded during the flight and tentatively attributed to Ozone clouds.

Attempts to determine the spectrum of the dipole anisotropy in the millimetric region have been carried out by the Rome-Florence Group by means of several balloon flights. The results are compared to COBE-FIRAS spectrum in fig. 37.

A collection of the most recent radio data has been prepared by COBE team and is shown in fig. 38, 39.

Maps of the dipole anisotropy became available since 1984: both Berkeley, Princeton and the Soviet Group of IKI provided maps of the sky at a sensitivity level of about 0.i mK where dipole anisotropy was the only CBR anisotropy clearly evident; see fig. 40, 41 and 42.

In the following we briefly discuss the use of dipole anisotropy as a tool for investigating spectral distortions [86-88].

Let us assume that the spectrum has some distortion AI(v), so that

5 8 13. M E L C H I O R R I and F . M E L C H I O R R I

galactic plane ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :~ . . . . . . . . . . . . . . . . . . ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " i

galactic i . . . . . . . . : . . . . . . i ........ i ~-

! . . . . . . . . . . . . . . .

plane

. ~ first string of data ~ .

................... i..:-: ........... i ................... i .............................. galactic ; ~ , l m e

(20 rain) galactic . . . . . . . . . . . . . . . . . . . . . . . . . . .

.- ............ ~. plane . . . . . . . . . . . . . . . . . . . . . . . .

galactic plane "

plane ....... !

idipole

i . . . . . . . . . i

ipolei galactic i

plane i .........................

. . . . . . . . . i - . - " -

. . . . . . . . . . i "-

i "

........... i.....!

galactic i i plane ................ i i

................ : . .! . . . . . . : . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 35. - Signal recorded from Florence 1978 balloon exper iment in the 700-2000 pin range. The dipole anisotropy has been observed directly in the data together with the signal due to the galactic plane. In the box to the right the scheme of the apparatus is shown: a wobbling p lane mirror c explores two sky regions 6 degrees apart (A and B). The radiation is collected by the bolometer through an optical system (not shown) having a field of view of _ 2.5 ~

w h e r e ~ = ( A I / I ) a n d ~D is t h s p e c t r a l i n d e x of t he d i s to r t ion a lone . In o r d e r to ge t s o m e a d v a n t a g e in u s i n g the d ipo le s igna l i n s t e a d of t he

a b s o l u t e va lue AI, one h a s to r e q u i r e that , e i t h e r ( ~ D / ( 3 - ~tot)) -> ( A I / I ) , or ( a n d ) ~Dfl >- 1: t h e s e r e q u i r e m e n t s c o r r e s p o n d , respec t ive ly , to a h i g h e r c o n t r a s t a n d / o r a h i g h e r s ignal .

T h e f i rs t r e q u i r e m e n t is j u s t

1 (57) > (3 -

In t he R a y l e i g h - J e a n s r eg ion of t he s p e c t r u m th is c o r r e s p o n d s to aD _> ( 1 / ~ )


0 90 180 270 0 90 180

0

galaxy

!! '

Azimuth 90 180 2'70 0 90 180

, I [ I I I I

b -39 -4 3 17 20 -39 -43

Fig. 36. - Signal observed in MIT experiment, where the sky is compared with a reference source. The dipole amplitude as expected from COBE data is shown: the offset of the signal is of the order of two mK and the stability of it is a major problem in this kind of absolute experiment.

and this condition becomes more and more severe as the distortion becomes smaller.

The first application of the dipole anisotropy is that relative to the comparison between FIRAS and COBRAS results. We may compare the dipole anisotropy spectrum, as measured by FIRAS to the dipole anisotropy spectrum as derived by COBRAS brightness measurements. This would allow us to decide if the fluctuations in the temperature recorded by COBRAS are real, or just due to the noise of the system. The procedure is illustrated in fig. 43a, b). Since the correlation between the two residuals (after removing 2.7 K dipole anisotropy) is very poor, one may conclude that COBRAS data must be within _ i0 mK all over the spectrum.

A second application has been shown in fig. 26, where possible distortions are shown. In the box of fig. 26 we have represented the same scenario but for dipole anisotropy, instead of for the brightness. We see that in the case of free-free distortion the dipole anisotropy changes sign, i.e. we predict a reverse in the direct ion, a r a t h e r pecu l i a r effect!

35 .3 . S e a r c h f o r t h e c o s m i c - b a c k g r o u n d n o i s e . Pho tons are bosons and, therefore , follow the Bose-Eins te in statistics, wh ich es tabl ishes that the m e a n square f luc tua t ion of the n u m b e r of pho tons in uni t p h a s e - s p a c e vo lume is given by

n 2 (58) An2 = + N '


10.0

7.5 I

}

5.0

O

2.5 Q

0.0

i i , I . . . . I , , L , I ,

7" ?,~

' ' ' 1 ' ' 1 1 1 ~ I1 ' ' ' Jl

7)

5 10 15 20 25 30 35 v(cm -1)

Fig. 37. - The dipole anisotropy spectrum, as provided by COBE-FIRAS, compared with the earlier wide-band observations of Florence-Rome Group 1) to 7).

3.8

3.6

v

~ 3.4

3.2

i �84 ~ ~ ~ ~ x"x,,~ L

3 . 0 . . . i . . . .

101 102 103 frequency (GHz)

Fig. 38. - A collection of recent (later than 1982) results on dipole anisotropy amplitude prepared by COBE team. �9 DMR <> Berkeley, A Princeton, [] RELIKT, x FIRAS.

whe re N is the total n u m b e r of i n d e p e n d e n t cells of the e l ec t romagne t i c field given by N = (8~v2 / c s) dr. This equa t ion was first der ived by Eins te in in 1909 [122].

At tempts to ver i fy the p r e s e n c e of the excess noise ~ = ( n 2 / N ) with r e s p e c t to the


51

50

r

~49

~9

~ 48

~ 47

46

! 45J

27{

§

I I l I , ~ ,

268 266 264 262 galactic longitude (degrees)

Fig. 39. - Same as fig. 38 but for dipole anisotropy direction (latitude, longitude).

20~

-2~ k -4o K

o 2 4 6 8 10 12 14 16 right ascension (h)

f

n Q 18 20 22 24

Fig. 40. - Map of the dipole anisotropy obtained by RELIKT I at 8 mm of wavelength: the contamination by our Galaxy is clearly shown.

Poissonian f luc tuat ions have been car r ied out by Alkemade et al, [123] and Kat tke and Van Der Ziel [124]. Those e x p e r i m e n t s are cons i s ten t with Bose-Eins te in statistics, a l though the poor sensit ivity of the detectors m a y ra ise some doubts abou t the rel iabil i ty of the results.

The power f luc tuat ions of a b lackbody m a y be rewr i t ten as

62 B. MELCHIORRI and F. MELCHIORR[

Fig. 41. - Map of the dipole anisotropy at 3 mm of wavelength obtained by Lubin (1979): Galaxy is almost undetectable at this wavelength.

X~

(59) AI~2 _ 4 c2h----- ~(kT)5 At] f

X I

x 4 exp [x] dx A f , (exp Ix] -- 1) 2

where x -- hv/kT, A f - - electrical bandwidth of the detector; AQ ---- optical trough- put. In the case of a body with an emissivity ~ < 1 the above equat ion is changed into [125, 126]

X2

A ~ 2 4 (kT) 5 I x 4 e x p Ix] -- 1 + g) (60) -- c~h~ AQ~ + (exp Ix] -- 1) 2

d x A f .

Xl

At first glance, noise measurements seem to provide the same informat ion as brightness measurements , with the (l imited) advantage of not requir ing radiat ion modula t ion and the (huge) disadvantage of having to detect faint signals: in the case of a 2.7 K blackbody, the expected power is of the order of

2 �9 10 -16 W / ~ / H z cm 2 sr in the band 800-2000 ~m. On the basis of this analysis the MIT group, after a pre l iminary investigation carried out by .Allen [127] decided not to fur ther proceed. De Bernardis and Masi [128] have shown that in the case of broad-band bolometers a single measu remen t of noise and brightness could allow to evaluate both the tempera ture and the emissivity of a gray body. Unfortunately,


60

30

o 0

-30

-60

north galactic spur

)rion Nebula

~ : '

22 4 10 14 right ascension (h)

unidentified structure

galactic centre .~

Fig. 42. - Map of the dipole anisotropy at 0.7-2 mm obtained by Florence Group (1980): the region indicated as ,,unidentified structure~ is the main responsible for a ,,quadrupoie- like,~ distortion of the dipole. An upper limit of AT_< 10 -4 K has been obtained in the region far from the galactic plane after removing the dipole gradient.

the low level of the expected signals requires the use of some method to disentagle the cosmic noise from the istrumental one. A correlation between two independent detectors may be used. In such a case the observed variance of the signal at the output of the correlator An1 An2 is proportional to the excess noise ~, while any information on the Poisson noise is lost [124]. The two terms, quantum noise and wave noise, are plotted in fig. 44 together with the spectral region explored in the Rome Group experiment. It consisted in a 10 cm Cassegrain telescope with 1.5 degrees of field of view (see fig. 45 and 46), cooled down to 1.5 K and a system of two 3He bolometers observing the same sky zone via a Mylar beamsplitter. Each bolometer was cooled by a separate 3He system, to reduce the cross-correlation between the two detectors. A shutter at 1.5 K was periodically inserted to measure the offset of the correlator. The entire system was tilted in elevation from 20 up to 50 degrees of elevation in two-degree steps to measure and subtract the atmospheric noise. At the end of each cycle measurements the dewar was tilted toward the zenith, where an ambient temperature blackbody provided the source for calibration. The electronic on-board correlator detected and ampli- fied the correlated noise of the two bolometers in the 1-60 Hz frequency region. The results, obtained in the course of two balloon flights, are shown in fig. 47. They allowed to put an upper limit of 3.1 K at l a to CBR temperature in the 0.8-2 mm region.

Despite the difficulty of the experiment and the relatively large upper limit, we

6 4 B. MELCHIORRI and F. MELCHIOI~RI

~ 5 - a) 7

'o #

0 5 10 15 20

7 O

. . . . I . . . . I . . . .

b)

T

. . . . I . . . . i . . . . I . . . . I 0 5 i0 15 20

v(cm -1)

Fig. 43. - a ) The spec t rum of the dipole anisot ropy as measu red by COBE (exper imen ta l data with er ror bars ) is compared with that expected from CBR spec t rum as measu red by COBRAS (cont inuous l ine), b) The two spect ra are compared after removal of dipole. The lack of corre la t ion between the deviations in the two spect ra allows to improve the accuracy in the t empera tu re de te rmina t ion by COBRAS.

10 ~

/~...~ ....

" / /J <: ii: ~ ~-,.. r 10 ~

N /' ""' :\"

o 10 2 /

2.7 K noise

O

10 ~

10 ~

wave noise :

i ! i i ill I

10 .2

\ , \

\

, ,,,,,,I , , ,, .... I i

10 -1 10 ~ 101 ~, (cm)

Fig. 44. - The photon noise of a 2.7 K blackbody is due to two components. The quantum noise (fluctuations in the number of photons) is not detected by the correlation between two detectors, while the wave noise in the shaded area has been observed in the Rome

experiment.


R

C

)D

c

(

~E

Y/2?/A

'WM

liquid 4He

S

Fig. 45. - Optical diagram of the Rome experiment: a small Cassegrain telescope (PM + SM) (20 cm in diameter) is immersed into liquid helium and separated by a Mylar window (MW) from the vacuum tight bolometric chamber where the beam is splitted into two parts by a mylar beamsplitter BS. Two ~He detectors (only one is shown) are employed to collect the radiation, each bolometer having a separate cryopump, in order to minimize the spurious correlations. A cold shutter is periodically inserted in the field of view to measure these residual correlations.

believe that it represents an important result, being the only one devoted to the time variations of CBR. It also provided the first direct measurement of the atmospheric noise in the 1-60 Hz region at balloon altitude. At present, ~He bolometers are sensitive enough to attempt the direct observation of the CBR noise by means of a single detector. The comparison between the two methods would provide the first check for the photon noise of a blackbody.


Fig. 46. - Details of the in s t rumen t before the balloon flight.

v

4 �84

/JJ 0 1 2

(sec 0) 2

I I I i

Fig. 47. - Results of the noise experiment: the correlated output of the two bolometers is plotted v s . the square of the secant of elevation. This allows to estimate the residual atmospheric noise, while the extrapolation to zero provides the value of the CBR wave noise.

THE COSM1C BACKGROUND RADIATION 67

4. - C B R p o l a r i z a t i o n .

Rees [164] was the first to point out that the degree of polarization plays for CBR anisotropies the same role that the study of spectral distortions has for primordial energy injections: as CBR is last scattered at Z = 1000, any anisotropy in the scattering will give rise to a linear polarization. This important consideration was not taken seriously by early observers because Brans [165] suggested that the polarization plane is rotated and scrambled when photons propagate in an anisotropic Universe. Only in 1978 the Florence Group in [166] showed that the rotation is negligible in all but patological anisotropic models and in [167] attempted for the first time to detect the polarization of CBR in the millimetric region. This wavelength was selected because Faraday rotation is large in the radio and the random galactic magnetic fields could erase the polarization.

The measurement of a tiny degree of polarization (much less than 10 -3) is a tremendous task even in the visible region. A variety of sources of spurious polarization are expected: in the millimetric region even the detector itself, being a crystal of Ge, is affected by an intrinsic polarization. The main consequence is that a fraction of the incoming radiation is spuriously polarized and modulated by the rotating wire-grid polarizer employed in Florence experiment[167]. The optical sketch of the instrument is shown in fig. 48. The optical system defines two

7 5 9 , 6 1%?02 1 4

N | i'

0

N

Fig. 48. - Optical scheme of the millimetric polarimeter employed by Florence Group in searching for CBR polarization in 1974: a Cassegrain system (primary mirror (2) plus secodary mirror (3)) defined a field of view of about 0.5 degrees, while a TPX lens (4) defined a larger field of view of 5 degrees. A rotating polarizer (21) modulates the polarized component only at about 10 Hz, while a polarized source (20) may be inserted in the field via telecommand. (Adapted from [168].)

6 8 B. MELCHIORRI and P. MELCHIORRI

fields of view of app rox ima te ly 0.5 and 5 degrees, respectively. A 20 c m p r i m a r y m i r r o r d e t e r m i n e d the smal les t field of view, while a 4 cm TPX lens was employed in the second optical channel . A heated, polar ized source m a y be inse r ted by t e l e c o m m a n d in the field of view, t he reby allowing a check of the p e r f o r m a n c e s in flight ( see fig. 49). Finally, the po l a r ime te r was m o u n t e d on a p la t fo rm cont inu- ously ti l ted f rom 10 up to 40 degrees above the horizon, in order to p e r f o r m a sky survey and to allow the sub t rac t ion of the a tmosphe r i c offset (due to a t m o s p h e r i c emiss ion spur ious ly polar ized) by m e a n s of the secan t law t echn ique (see fig. 50 and 51). After subrac t ing a tmosphe r i c res iduals (see fig. 52) one has [168]

(61) P = = (3 -t- 4) �9 10 -4 , c~ = (180 _+ 35) ~

-~ p

5 = ( - - 57 _+ 22) ~ , 22 = 30 (13 ) .

The poor degree of conf idence suggests to take the value of P as an u p p e r limit.

pos. B

24 . . . . 22

17 18

10

]

Fig. 49. - Optical and mechanical scheme of the on-board polarized source for calibration. The source consisted of a piece of polarizer over a small piece of Eceosorb, heated by a resistor to a known temperature. The source could be inserted in the field of view by activating a magnet via a telecommand. In this way a calibration of about 5% of accuracy was achieved in the polarization experiment of Florence Group.


Fig. 50. - Two views of the gondola with the polarimeter ready before the flight.

200

o~ 150

'~ i00

50 2

A) oo /~UT 18 a6 /

f I I I I I I B I I

4 6 8 10 12 (sin a) -1

B )

\

2P5 , , I _ _ 20 30 35 40 5 (degrees)

UT 18 a6 RA 17.95 UT 1900 RA 18.45 uT 1930 RA 18.90 UT 2000 RA 19.40

Fig. 51. - A) Signals recorded as a function of the elevation angle: the effect of the spurious atmospheric contribute is estimated by curves a) and b). The observed curves are therefore difficult to explain. In B) the residuals are plotted, after the best fit for atmospheric emission spuriously polarized by the instrument. If interpreted as due to a polarized sky emission, the observed signals would require a degree of polarization of CBR of about 10 -4, too large to be believable. It was used as an upper limit[169].

All the o ther m e a s u r e m e n t s of polarizat ion have been car r ied out in the radio region with uppe r limits comparab le with that a l ready repor ted [169-171]. Finally, in 1983 Lubin et al. obtained an upper limit of few units in 10 -~, which is still the best available upper l imit[172].

Theore t ica l implicat ions of CBR polar izat ion have been discussed in the f ramework of anisotropic cosmic models by Basko and Polnarev [173], Negroponte and Silk [174] and, more recen t ly by Fabbri and Milaneschi [175]: these analyses, & la m o d e in the eighties, are now less interest ing, as the universe seems to be very close to the s tandard isotropic model pred ic ted by Fr iedmann .

Despite the fact that CBR polarizat ion has still to be detected, its potent ial i ty as cosmological tool has been poin ted out by Ceccarel l i et al. [168]: by studying the Faraday rotat ion of the polarizat ion plane at different wavelengths one would be


Fig. 52. - The first millimetric flux collector devoted to the study of CBR anisotropies was realized in 1974 in collaboration between Florence Group and Torino Group of Cosmogeofisica and located at the Alpine station of Testa Grigia. The collector was 2 m in diameter with a wobbling secondary, as shown in the picture. It was able to set the most stringent upper limit at an angular scale of 20 arcmin.

able to m e a s u r e the in tens i ty of the ext ragalact ic magne t i c field, if any. The discovery of a cosmic magne t i c field would have in Cosmology an i m p a c t c o m p a r - able wi th the discovery of CBR itself.

More recent ly , CBR polar iza t ion has again a t t rac ted the a t t en t ion of cosmologists, b e c a u s e a ce r ta in a m o u n t of polar iza t ion is expec ted in the case of CBR aniso t ropies p r o d u c e d by gravitat ional waves. The p red ic ted level is, however , well be low the l imits al lowed by p r e s e n t technology.


5. - C o s m i c - b a c k g r o u n d a n i s o t r o p i e s .

51. Early observations. - Searches for CBR anisotropies carried out during the first ten years after the discovery of CBR (1965-1975) can be roughly classified in large-scale and fine-scale experiments. We have already described the search for the dipole anisotropy. The next step was represented by the quadrupole pattern. The interest for a quadrupole anisotropy dates back to the Bianchi classification of possible anisotropic space-times, re-arranged in a modern shape by Estabrook et al. [191]: all the anisotropic homogeneous models predict a significant quadrupole and the hope of cosmologists was that of evidentiating some global anisotropy in this way.

On the other side, fine-scale searches aimed to exclude non-cosmological origins of CBR. As a matter of fact, in a variety of alternative models, it was proposed that CBR arises from the integral along the line of sight of the radiation produced by many sources at different red-shifts, see for instance [116]. Smith and Partridge [176] have been the first to point out that all these models predict significant small-scale fluctuations, as the beam size approaches the single-source count. It was customary, following their work, to present the upper limits obtained in anisotropy experiments in terms of a parameter # given by

/ A / ~ 2 number of sources per volume

(62) # = Nf2 ~-]- ) oc number of sources per solid angle'

or, alternatively, to quote the minimum number of sources required to explain the observed degree of isotropy. For instance, Boynton and Partridge results of 1973 implied a minimum surface density of sources of 1011 sr -1 [1771.

Particularly impressive was at that epoch the systematic work of Parijskij who was able to set stringent upper limits ( ( A T / T ) _< 3 �9 10 -4) at the angular scale of 1-10 arcmin and at 3.95 tin of wavelength [178], as well as the already quoted work of Boynton and Partridge[177] at 3.5 mm of wavelength and 80 arcsec ( ( A T / T ) <__ 2 �9 10-3).

Limits ranging between 10 -~ down to 10 .4 have been obtained by various authors during the decade 1965-1975 [179-186]. Some authors have added sparse considerations about possible physical implications of the observed upper limits [117]. To this purpose, the more often considered theoretical papers were those of Rees an Sciama (1968), dedicated to the CBR anisotropies produced by large primordial inhomogeneities [188], or the work of Chibisov and Ozernoy (1970) discussing the Compton interaction between CBR and moving ionized perturbations [189]. In our opinion the most important contributions in this period lie in two fields:

1) A continuous improvement in data handling and analysis: Princeton Group (Boynton and Partridge [177]) has paved the way for the very sophisticated statistical methods later on applied to CBR anisotropy experiments. A first naive attempt to improve the upper limits on A T / T w a s that of Parijskij [178]: he plotted the r.m.s, values of A T / T vs. the integration time and extrapolated it to infinity. This partiaIly erroneous method (the data are correlated) was later on substituted by the Neyman-Pearson test[177].


voids great attractor super clusters 102 101 10 ~

+

clusters Mpc

............ ! . . . . ~__ . 27. ~:2:2

.................. i - '::::2::

i �9 7 - - = r -

101 10 2 103 1 (wavenumber)

Fig. 53. - Fourier plot of CBR anisotropies. The quantity (1/4TO) l (2 l + 1)Ct in ordinate represents essentially the power of < (AT~T) 2 > at the angular scale --~ l - ' rad (see text for details). At large angular scales (small l) the spectrum expected from Sachs-Wolf effect is fiat. For l ~ 100, the size of the perturbations at decoupling (Z = 1000) becomes smaller than the horizon and the effect of peculiar velocities due to gravitational attraction increases the level of anisotropies via Compton scattering. Various curves are represented as a function of the parameter h = normalized Hubble costant (h = 1 corresponds to H = 100 K m s - ' / M p c and of the barionic matter content normalized to the critical density. In the lower part of the figure we have reported the transfer function of various experiments: for each experiment the cut at high l values is due to the finite beam size (perturbations much smaller than the beam size are averaged). For low values of l a cut-off is determined by the finite amplitude of modulation. 1) FIRS, 2) COBE, 3) Tenerife, 4) ULISSE, 5) South Pole, 6) ARGO, 7) MSAM (2 beams), 8) MAX, 9) MSAM (3 beams), 10) TIR, 11) OVRO.

2) The in t roduc t ion of bo lomet r ic t e chn iques in the field by F lo rence Group, and MIT. The p a p e r of Cadern i et at. [187] of 1987 was the first in descr ib ing the use of an in f ra red bo lome te r at the focal p l ane of a h i g h - m o u n t a i n te lescope dedica ted to the sea rch of CBR anisot ropies (*) ( see fig. 53). The

(*) The realization of a millimetric telescope dedicated to the search of CBR anisotropies was proposed by the Florence Group to GIFCO (Gruppo Italiano Fisica Cosmica) in 1974, but the proposal was modified by the Milan Group into a near-infrared telescope (still


authors worked at angular scales of 25 arcmin in order to study the density fluctuations responsible for the formation of bound systems, like clusters and superclusters of galaxies. The upper limit they found of 1.2 �9 10 -4 was therefore translated into an upper limit for the red-shift Z at which the corresponding perturbations have reached a contrast (Ap/p) = 1. It turned out that in the case of adiabatic perturbations, clusters of galaxies should have reached such a value at Z___ 0.5 a very tight constraint which clearly indicates the presence of a problem. This work was followed in 1978 by a set of airborne flights on board of NASA Convair 990 dedicated to the search of anisotropies at angular scales of two degrees, again by means of a far-infrared bolometer [190]. The authors used two lock-in's 90 degrees apart in phase, in order to record simultaneuously signal plus detector noise and detector noise alone. A technique which anticipated that used by COBE in DMR experiment, where two radiometers are observing the same sky region and the difference between the two outputs provide information on the detector noise.

Apart from these progresses, the first ten years of research may be described as a slow but continuous improvement in the upper limits to CBR anisotropies at all the possible angular scales and wavelengths. A significant change in this trend occurred at the beginning of the eighties, when two experiments carried out by the Princeton Group [192] and the Florence Group [193] indicated the possible detection of both a quadrupolelike anisotropy[192, 193] as well as anisotropies at angular scale of 6 degrees [194]. Immediately, several authors attempted to explain the results in terms of anisotropies induced by matter perturbations. While very soon the quadrupole pattern disappeared from radio data and was interpreted as due to cold dust in millimetric data, the anisotropies at angular scale of 6 degrees survived up to the present and in view of recent COBE-DMR data they may be interpreted as the first detection of CBR anisotropies.

5"2. A semi-empirical description of CBR anisotropies. - We have already discussed the case of dipole anisotropy: CBR temperature is expected to be non- uniform in the sky, with a spatial distribution described by

(63) T = To (1 + / ? cos O + / /2 cos 2 0 + ...),

where O is the angle between the direction of observation and that of the maximum amplitude of dipole (direction of motion).

An alternative way for describing this anisotropy is that of expressing it in terms of spherical harmonics. This is a very natural way, the spatial distribution of CBR being observed on the sphere of the last scattering surface. Let 1 and b be the new galactic coordinates (*). The space distribution of T is given by

operating at Gornergratt, in the Alps). Florence Group and Torino Group decided to build a low-cost far-infrared flux collector, located at Testa Grigia, 3500 m above sea level: it was successfully employed in the search for CBR anisotropies. (*) Galactic coordinates are usually indicated as /II, bII to distinguish them from the old ones, where the position of the galactic centre was slightly displaced: we have removed II for the sake of simplicity.


(64) T= Too + To, cos/cos b + T,o sin/cos b + Tn sin b +

+ To,2(~sin~b--~)+Trzs in2bcosl+ T,).~sin2bsinl+

T + 72o cos" b cos 2l + T2,). cos ~ b sin 2 l ,

where the coefficients T~y take into accoun t both the dipole (i, j---* 01, 10, 11) and the quadrupole terms. The most precise m e a s u r e m e n t of the dipole coefficients is that of COBE-DMR [1341]

Tot -- T.~ = -- 200 + 27; T l o = - - 2216 + 67; T n = 2406 +__ 66 gK.

Obviously, the ent i re sky distr ibution of CBR may be descr ibed in te rms of spher ical harmonics :

l = O 0 ?viral

(65) T= E E ar r ~ ( o , , l = 0 r n = - - l

where the'. first t e rm of the sum A~176 = To = 2.73 K is just the CBR m ean t empera tu re , averaged over the sky. The coefficients A~" are just the numer ica l values necessa ry to describe the observed sky pat tern: it is clear however, tha t they should be in some way related to the physical mechan i sms responsible for CBR anisotropies. Let us forget for the m o m e n t this last point and re-ar range the express ion in a more comfortable way. We may rewrite eq. (65), by posing A T = T - - 7'o and a'l '~= (1 /To)A~ '~, as

AT l ~ o o ~rt = t

(66) - - = E • a'~Y~(O, 45), T o / = 1 m = - l

where we have to under l ine that now 1 start, f rom 1 and not f rom 0 as before. Let us assume that we explore a cer ta in sky region: we are in teres ted in the r.m.s. value of the t e mpe ra tu r e fluctuations. There fo re we have to compute the quant i ty < (AT~T) ") }. We may write

(67) 2} 'f( l = ~ (O, 45) dr2 =

]m

- "~ Y,~,(O, qb) df2. 4~ y~ }2 a, a,. J Y. , (o , r '"

! ! The integral of spherical ha rmonics is zero unless l = l , m = m , so that

(68) = 2 Z 4~ . l m


In a uniform Universe we expect a rotational invariance of the coefficients, so that the sum over m simply gives 21 + i and, finally we get

(69) = ~ 4~ ' z

where the coefficients Ct = ( l a ~ l ~ } are the quantities we want to evaluate. Theories of galaxy formation provide information on the dependence of these

coefficients on l: the normalization, however, is mainly experimental. It is customary to plot the quantity ~t = l(21 + 1) Ct vs. l just because in the most popular theory of cold dark matter plus inflation ~ is expected to be a constant for larger-than-horizon anisotropies. In fig. 53 we have plotted some of these ~,theoretical power spectrw~ just to give an idea of the variety of the possible theories. We will return to this plot at the end of the next subsection, after the discussion on the connection between ~z and the theories of galaxy formation.

For the moment let us investigate the effects of the instrumental limitations.In the practical cases, one has to introduce an instrumental function F(l, 6), 6) which depends on the beam size a (for a Gaussian shape of the angular response,

is just the variance), on the beam modulation amplitude (two or three sky regions are observed, separated by an angle O) and on the type of modulation (two beams, three beams, sinusoidal, square wave, etc.). In the two simple cases of square wave, two- and three-beam modulation the instrumental function is of the type

(70) F(/)t~obeams ---- [1 -- Pt (cos O)] exp [-- a212],

(71) F(/)t~,r~b~, = [3/4 -- PC (cos 20)] exp [-- a2/2],

where Pt (cos O) are the Legendre polynomials: for large l they tend to the Bessel function J0 ((l + 1/2) O). In fig. 53 we have illustrated how the transfer function changes for different experiments: they would probe different regions of the power spectrum and, as an obvious consequence, also different mechanisms responsible for them.

5"3. CBR anisotropies and galaxy formation theories. - It is well known that a large part of the modern Astrophysics is based on the solution of the Boltzmann transport equations or the equivalent Liouville equations; for instance, when applied to stars, these equations allowed to study the flow of the stel larf iuid, i.e. matter and photons, from the central core to the surface, to the interstellar space up to the observer. It is not surprising, therefore, that a similar approach has been attempted in Cosmology, with the important difference that the relevant transport equations have to be written in the framework of the curved space-time. If we write and solve the BTE for the cosmic fluid (matter plus photons), we get the evolutionary story of the Universe with a degree of approximation which depends on the schematization we adopted for the fluid and the type of interactions inserted in the ,,source term,, of BTE. For instance, if we assume a Friedmann model for the Universe (so that isotropy and homogeneity are granted) and introduce in the source term the contributions by cosmic dust and gas, we get the CBR spectrum plus distorsions. If we apply BTE to fluid perturbations Ap/p and

7 6 B. MELCHIORI~I and F. MELCHIORRI

An/n (where n are the photons of CBR) we get the evolutionary story of matter perturbations up to galaxy formation and the corresponding story for the CBE photons spatial and spectral distribution, usually referred to as CBR anisotropies. The problem is a bit more complicate than this, however.

The mathematical and physical problems can be summarized in the following steps (see Bond [139]):

1) Choose a model of Universe ( ~ = 1; 0.1 etc. degree of anisotropy, inflation, reionization, etc.).

2) Choose a gauge, background metric and equations.

3) Write the BTE for all the fluids (photons, baryons, exothic particles...)

4) Choose the spacelike hypersurface on which the perturbations have to be estimated.

5) Choose the initial spectrum for the perturbations.

6) Expand the perturbation equations in a complete orthonormal set of spatial eigenfunctions (a sort of Fourier analysis) and solve the BTE equations.

7) Normalize the results to the present-day amplitude of the perturbations.

8) Convolve the computed modes for photon distribution with the angular response and type of sky modulation of each observation in order to compare the theoretical expectations with the observations.

Let us discuss few important points to some extent. First of all, it appears natural to study the evolution of the amplitude of the perturbations separately for each scale. As long as the perturbations are small, i.e. (Ap/p) << 1, it is conventional to expand density inhomogeneities in a Fourier expansion

Ap (72) - (2=)-3 | 5kexp [ - ikx] d3k,

P J

where the wave number k is measured in a comoving reference system and it is related to the physical wave number kphys simply by kphys = k /R( t ) . We can measure k in Mpc-1 a unit which immediately relates k to the typical comoving dimensions of the perturbations under study. To make this unit more realistic, we can assume R (t) = 1 at the present time, so that we can refer immediately k to the dimensions of the perturbations today (to be more precise, 1/k provides the present-day dimensions, ff the perturbation is still in linear regime, i.e. (Ap/p) << 1).

The quantity 5k is not the most useful quantity, however. What we need is an estimate of the average over all the sky of Ap/p. A bit of Fourier algebra and the use of the Parseval theorem provide the result

(73)

QO


The contribution to the density contrast from a given logarithmic interval in k, d k / k = d Ink = 1 is, therefore,

(74) (A~) -~ (2u)k - 3 k 3 / 2 ] ~ k l "

Incidentally, we note that the above quantity

contrast, i.e.

coincides with the mass

It is also customary to express ~k in terms of power spectrum, i.e. 15~1 oc k ~, where n As an appropriate spectral index. By changing the sign and the value of n, one can add power to small or large scale and can try to fit the present-day spectrum of the perturbations. Therefore, we get

tA_pp~ A M k3/2 ` ~/2-~/6 - - ~ ~ k [ oc M - \ p ] M

The last relation derives from the fact that k ~ M -1/3. This formalism is what we need to perform, but a word of caution is appropri-

ate; if the Universe has Q < i, the evolution of the perturbations occurs in a curved metrics (obviously this is true also for ~ > i, but this case is considered of scarce relevance, being cosmologists still unable to find matter enough to get

--- I). At this point the modes are no more conserved as plane waves; the effect of the curvature is obviously more pronounced for large scales. It is customary to express this fact An terms of angular scales O in the sky; the above formalism holds for ~ = 1 and provides reliable results also for ~ < i, providing that we limit our analysis to scales O _< (E2/2)/(1 -- E2-1/2).

This last point led us directly to another important problem, namely the distinction among the perturbations depending on their scale with respect to the horizon.

Perturbations larger than the horizon are evolving like independent Universes, physical processes inside being unable to propagate over the entire perturbation. As the perturbations enter the horizon, gravity, as well as other physical processes become relevant. Ths situation justifies the decision of cosmologists of giving the amplitude of density contrasts as the relative perturbations cross the horizon.

This long and perhaps boresome discussion As necessary in order to understand the delicate points 2) and 4) of the mathematical programme listed before. For perturbations smaller than the horizon, a Newtonian analysis is adequate [140, 141], but as they approach the horizon the effects of tile curvature dominate; beyond the horizon, physical effects are unable to influence their evolution which is essentially kinematic; ,they evolve like a wrinkle in the fabric of space-time,, (Turner [149]). One consequence of this fact has been already discussed when we limited the validity of the Fourier decomposition. But the problem is even more serious; one must be very careful in the choice of the gauge system:

78 B. MELCH[ORRI and F. MELCHIORRI

quantities like Ap/p are not gauge invariant under general coordinate transformation. In fact, it can be shown that through an appropriate choice of gauge transformation it is always possible to make 5p = 0. One has to worry about spurious gauge modes ,lurking in the computer ready to attack the unwary>> (Bond [139]). Two ways have been followed in the literature: the first one dates back to the seminal paper of Lifshitz[148], where a synchronous gauge (g00 ---- -- 1, g~0 ---- got ---- 0) was selected; this way is dangerous and one has to work very carefully, as pointed out> for istance, by Press and Vishniac [150]. Lifshitz himself has shown that two of the four modes in his computations are gauge modes. Despite these difficulties, a lot of important results have been obtained in this way; a sinchronous gauge has been adopted, among others, in the papers [151-154].

In 1980 Bardeen [155] has pointed out the danger of the choice of hypersur- faces (on which the perturbations are estimated) which suffer from large warpings along the evolution; he introduced a set of gauge-invariant variables (in the contest of cosmological perturbations <<gauge invariance>> means an invariance under infinitesimal coordinate transformations). The most famous of these gauge- invariant quantities is ~ = A p / ( p + p) which remains constant for perturbations larger than the horizon.

We do not want to investigate this problem further; for the interested reader we refer to the review of Bond [139] and the references listed therein, or to the Peebles book [147].

Let us return to the problem of the <<initial spectrum of perturbation>>. Once we have clarified the different meaning of the perturbations depending on their scale, the question remains as to what is the initial spectrum and what mechanism was responsible for it.

A special spectrum, often quoted in the literature, is the so-called <<scale-invariant, spectrum, or <<Harrison-Zel'dovich>> spectrum. This is a spectrum in which (Ap/p)~ is constant and independent of the scale, when entering the horizon. Now, if one recalls the property of the previously described gauge- invariant quantity [, we have that

(76) [Ap/(p + p ) ] , = , , , ,-, [Ap/(p +

where tl is a generic time before the horizon-crossing. In the radiation-dominating era (p +/9) = 4/3p, therefore, apart from a constant, once the scale invariance is granted at the horizon, it holds also before it. This fact allows us to describe the condition of scale invariance as

(77) (Ap/p) H = k3/2 II 5k II (2u) 3/2 = const.

If we recall the definition 5~ -- k s, we have the spectral index n = -- 3. One has to stress that this is the spectral index for a scale-invariant spectrum when the perturbations enter the horizon, and not that of the perturbations at a given time. In order to connect the horizon-crossing modes with that at a given time, one has to specify a gauge; in the synchronous gauge we have

(78) / -2j3


and the corresponding spectrum is

If we put ct -- 0 as requested for Harrison-Zel'dovich spectrum, we can use the above relation to compute n and we find n -- 1. So both n -- 1 and n -- -- 3 are often quoted in the literature.

This spectrum was introduced by Harrison in view of a ,,cosmic democracy~ (all the scale should have the same chance) and it turned out to be appropriate in order to have perturbations great enough to produce galaxies and not larger structures.

Obviously, every spectrum is allowed, if we find out some physical mechanism which produces it. Since all the perturbations at times early enough are larger than the horizon, it seems impossible to find any p h y s i c a l mechanism.

How many types of these larger-than-horizon perturbations exist? Let us consider the simple case of a Friedmann universe. Two global ,,quantities~ can be perturbed to obtain larger-than-horizon fluctuations, namely the curvature K and /or the equation of the state p = p~ + 1/3fir. In the first case (curvature perturbations) there is no a pr ior i reason to perturb a specific species of particles more than another. Therefore, we give the same amount of perturbations to all the species present. If nb, nx, np are, respectively, the number densities of baryons, x-particles, photons, we fix

5nb 5nx 5np

n b n x Up

It is easy to understand the nature of such perturbations; if we compute (nb/np) by taking into account the above condition we get 0. This means that the

fluctuations per entropy density vanish; i.e. these can be called adiabatic perturbations. The net effect of these perturbations is that of changing the energy plus matter density locally, i,e. that of changing the curvature K locally in the Friedmann universe. Therefore it is also correct to call them curvature per turbat ions .

The second possibility is that of perturbing the state equation locally, without changing the curvature. This is possible because the equation of the state is dominated at early times by the radiation pressure term, i.e. p = pr /3 . Let us assume that we have matter density fluctuations 5pro which are energetically compensated by radiation fluctuations 5Pr, so that the total fluctuations 5 = 5pm + 5pr---= 0. These fluctuations do not change the curvature, but still change the equation of state by the amount 5p = 5pr/3. They are called i socurva- ture per turbat ions: they are close to be isothermal, since in the radiation-dominating era a very small increase in temperature is required to compensate locally a mass overdensity. One should note that these perturbations when entering the horizon have the radiation part dissipated (if the horizon-crossing is in the radiation-dominating e r a ) o r radiated away and the remaining mass contrast evolves like the case of pure adiabatic perturbations. Therefore, the distinction between isocurvature and curvature perturbations make sense only in


the early Universe, when we are dealing with larger-than-horizon fluctuations. A striking difference is present in the early times; isoeurvature perturbations have no evolution as long as they are larger than the horizon, just because they are not affected by the metric evolution, which in a sense does not recognize their existence.

Curvature and isocurvature perturbations are the two cases which are currently investigated in the literature for primordial fluctuations. They relate to the metric (curvature) or to equation of state: both these quantities are ,global,, in the sense that no typical scales enter in them, therefore, perturbations of the metric and /o r the equation of the state are able to produce fluctuations larger than the horizon.

An important change to this picture is produced by inflation. The basic idea of the inflationary scenario is that there was a time in the hystory of the Universe when the vacuum energy dominated the energy density of the Universe. This fact allows to change drastically the evolutionary hystory of the Universe. In our case what is changing is the time evolution of the size of the horizon. We have already seen that in the case of standard Cosmology the size of the horizon is roughly proportional to H-1. During the inflation this quantity remains constant. It follows that each perturbation now crosses the horizon twice. It is inside the horizon at very early epochs, it goes outside it during the inflation and it crosses it again later. When inside the horizon physical mechanisms can set up perturbations of appropriate amplitudes; therefore, one has no more the necessity of postulating primordial kinematic perturbations.

In order to realize the inflation, one has to postulate the existence of a scalar field �9 the physical origin of which can be traced back to modern theories of particles physics. For our purposes it is interesting to note that such a field cannot be perfeetiy uniform. Computations of the quantum fluctuations of this field have been carried out by many authors. These quantum fluctuations give rise to density perturbations at the same scale of the order of

(80) ( A p / p ) h ~- H a / ~ .

The crucial point is that during the inflation phase the scales of relevant astrophysical interest (0.1 to 100 Mpe) cross outside the horizon in a very short time, so that both �9 and H can be considered constant along this period; therefore the right quantity of the above relation remains almost constant, thereby producing a scale-invariant spectrum of perturbations. Once outside the horizon, they evolve kinematically in the way predicted by the gauge invariant ~, i.e. they preserve the scale invariance and therefore re-enter in the horizon with the same property. It is natural to have curvature perturbations, scale-invariant by inflation. It turns out very difficult, although not impossible, to reconcile inflation with isocurvature perturbations, so that they are sometimes called not hones t to God.

The connection between the primordial spectrum of perturbation and that evolved at the last scattering surface requires a significant amount of calculations: the interested reader may find them in the Bond and Efstathiou work [137-139]. Usually, the spectrum contains an arbitrary constant which is normalized to the present density contrast by requiring that the mass fluctuation variance in a sphere of 8h -1 Mpc is b -2, where h is the Hubble constant normalized to 100 km/ s /Mpc and b is the biasing factor which defines the amplitude of


perturbations below which galaxies are not formed (typical values of b range between 1 and 2).

Once the perturbation spectrum is determined on the the last scattering surface, the evaluation of the effects on the spatial distribution of CBR is straightforward.

Let us start with perturbations larger than horizon at decoupling. For these perturbations Sachs and Wolfe [129] have indicated the following relation:

(81) - + ~ s + ~ ~ ( x , t) dt, T 4 rad

where the first term measures the radiation density fluctuation at the last scattering surface, the second term takes into account the gravitational shift in frequency due to the gravitational potential �9 at the last scattering surface and the last term is an integral along the photon geodetic from the last scattering surface to the observer, r being the gradient of gravitational potential. Under the hypothesis of curvature perturbations (adiabatic perturbations), ~2 = 1, the first term is almost constant and is given by

rad 3

Since ~ is constant in this case we get

AT 1

T -- 3c 2 ~ '

This is usual equation quoted for CDM plus inflation model, in which adiabatic perturbations are expected. A measurement of CBR anisotropy is then directly related to the density contrast Ap/p through the Poisson equation

1 (83) - - A2q5.

R( t ) 2

Stebbins [201] has pointed out that the general Sachs and Wolfe equation is useful to describe other galaxy formation scenarios. It is clear that in the case of isocurvature perturbations, larger-than-horizon anisotropies are very small, just because radiation fluctuations compensate matter fluctuations. This is the only qualitative statement we can make in this case, isocurvature perturbations being much less defined than curvature perturbations (the initial spectrum is arbitrary). In the case of anisotropies arising after decoupling (like those due to primordial seeds as strings) the last term of the equation becomes important and

(84) --_AT ~ qb, T c 2

where now the gravitational potential is that due to the seed.


In the SW equation we have neglected the possible contribution of gravitational waves. These tensor modes have the practical effect to increase large scale fluctuations without changing significantly t h e slope, as shown in fig. 58.

Therefore, as far as larger-than-horizon anisotropies are concerned, we may conclude that GW are indistinguishable from curvature perturbations.

Let us now consider perturbations smaller than the horizon: another source of perturbation is now at work, due to the fact the perturbations are causally connected. We expect a Doppler effect due to the infall of perturbations into the gravitational potential wells of the last scattering surface (the amplitude of anisotropies will be proportional to the peculiar velocity field, i.e. A T ~ T = n • Yr.

It is interesting to note that this effect is due to baryonic matter moving under the influence of gravitation: later on, when baryonic matter is trapped into the potential well of non-baryonic matter, any signature of the primordial distribution of baryonic perturbations is lost. Therefore, as correctly pointed out by Novikov [202], this region of angular scales is the only one which allows us to investigate the baryonic primordial perturbations. The main conclusions of our analysis are the following:

1) Measurements of anistropies for scales greater than the horizon at Z = 1000 (a >_ 5 ~ would detect the effects of the gravitational fluctuations on last scattering surface. If the picture of grmdtational instability is correct, we expect an amplitude of the order of 30 ~tK, largely independent of the details of the models.

2) Around 0.5 ~ there is the largest contribute of the Doppler effect, which significantly depends on several parameters, like b, Q, •b etc. Therefore, measurements at these angular scales will provide precious information on the physical properties of the process of galaxy formation.

3) At angular scales much smaller than 0.5 ~ the thickness of last scattering surface becomes greater than the radial dimension of the single perturbation. The fluctuations are therefore averaged along the line of sight and the amplitude of the observed anisotropy falls. Therefore, the theo l , of gravitational instability does not anticipate significant anisotropies at these small angular scales.

Recently, a new source of p r i m a r y anisotropies has been suggested: Some inflationary models predict non-scale-invariant fluctuation spectra and significant amount of gravitational radiation [142-145]. It follows that tensor perturbations (gravitational waves) may significantly contribute to CBR anisotropies. Generally speaking, this hypothesis offers an additional parameter to fit the anisotropy data already available.

All the above considerations are summarized in fig. 53, where the expected behaviour of C~ is shown for some peculiar cases. In the same figure we have plotted the transfer functions of several on-going experiments, which clearly probe different regions of the power spectrum. In order to distinguish from the various physical situations, one not only has to provide enough sensitivity, but must be also able to remove all the possibile spurious contributions to the observed signals.

Before concluding this by no means exaustive review, it is necessary to recall the possible interactions between CBR photons and matter for Z <_ 1000. We have already realized that if the Universe is reionized at a red-shift large enough (let us


say Z>> 20) an efficient Compton scattering would erase anisotropies: this is true, but only for angular scales smaller than horizon.

Let us investigate the effects of structures in the nearby Universe on CBR, assumed to be otherwhise isotropic. For Z ~ 10 the absorption by matter is negligible, even if it is fully ionized. Still CBR photons could be affected by the gravitational potential of large structures as well as scattered by local clouds of hot electrons, as in the case of the hot plasma present in custers of galaxies.

To be more precise, CBR brightness will be affected by temporal changes in the gravitational potential occurring during the time spent by photons in passing through the structure, up to the observer. We may write [130]

(85) - - = 2 dr T

where r is the gravitational potential, ~ the proper time and the integral is therefore carried out along the geodesic, from the last scattering surface up to the observer. In a sense, these are the minimal anisotropies we may expect on CBR and their existence is guaranteed by the presence of huge mass concentrations in the nearby Universe, like the so-called great attractor [131, 132] or large mass deficiencies, like cosmic voids [133]. The effect of voids is relatively smaller, due to the fact that the maximum density contrast cannot exceed --1. The amplitude of the expected anisotropies has been computed by Martinez-Gonzales and Sanz [130] in both cases of compensated and uncompensated concentrations (i.e. overdensities surrounded (or not) by a zone of mass deficiency). They turned out to be much smaller than 10 -5 unless a Swiss-chease model of compensated overdensities is adopted, where ( A T / T ) - ~ 3 . 1 0 -5.

Therefore, apart from patological cases, one is led to the conclusion that ,docal,, sources of anisotropies induce negigible effects on CBR.

The inverse Compton scattering in clusters of galaxies is called SZ effect (8unyaev-Zel'dovich effect) and has been widely studied in the literature. The effect is the same as the y-distortion already discussed in the subsection devoted to spectral distortions, but now it occurs in a limited region of the sky, i.e. over the few arcminutes where hot gas is present. It follows that an observer can detect it as a spatial difference inside and outside the cluster. Sunyaev and Zel'dovich were the first to realize the potentialities of such an effect [156], while the peculiar spectral behaviour of the spatial difference (positive in the submillimetric region and negative in the radio region) was first pointed out by Aiello et al. [157] in 1978. The use of the SZ effect to measure the Hubble constant in an evolution-independent way was first proposed by Cavaliere et al. [158], while Fabbri et al. [159, 160] suggested to employ it in precise measurements of CBR spectrum and in the determination of the deceleration parameter %. The basic properties of this peculiar anisotropy may be summarized as follows. In a cluster of galaxies the intracluster gas can be modelled in such a way to give a free-electron distribution of the type [161, 162]

(86) n e(r) = n e(O) (1 -~ r2 / r 2)-8/2fl

where r.m is the core radius, ne (0) is the central electron density, fl is an


appropriate exponent ~ 0.68. Due to the interaction between hot electrons and CBR photons we expect a temperature shift which is wavelength dependent:

h v (87) A T ~ = AT 0 (x ~ coseeh 2 (x ctgh x -- 2)); x --

KT '

where ATp~ represents the difference in antenna temperature toward the cluster and outside it [163], and AT0 is the difference at zero frequency. It is clear from this formula that the signal changes sign around the peak of CBR.

Finally, we have to underline the recent computations carried out by Maoli, Melchiorri and Tosti [146] on the possible contribution by primordial molecules: A certain amount of primordial molecules is expected to form in an otherwhise neutral Universe (see, for instance, Dalgarno and Lepp [206]): the abundances will be quite modest, however. For instance, LiH abundance cannot exceed that of Li itself, i.e. about 1 0 - 9 1 0 -s that of the hydrogen. Under these circumstances the collisional excitation and de-excitation will be negligible, so that emission and absorption are expected to be well below 10-5"IcBR, where ICBR iS the CBR brightness at t h e relevant frequency. Both CBR spectrum and anisotropies are pratically unaffected by this tiny effect. The situation could be different if CBR spectrum had some intrinsic distortion, because molecules may act as heat pumps, exchanging energy between rotational and vibrational levels. One could even argue if the perfectly Planckian shape of CBR spectrum is due to this molecular action: in any ease molecules tend to restore the blackbody spectrum and do not add detectable distortions. The remaining effect is the Thomson scattering which obviously does not alter CBR spectrum, but could in principle smear out the primordial spatial distribution of CBR: also in this case one should note that for a given molecular line and linewidth, each photon may be scattered only within a restricted range of red-shifts, when its red-shifted frequency falls into the spectral width of the line, i.e. A Z / Z ~ Av/v. So, at first glance, the paucity of molecules and the limited path of interaction suggest that elastic scattering is also irrelevant. One should recall, however, that in the case of a harmonic oscillator the Thomson cross-section is given by

8~ ( e2 "/~ v 4

(88) 6mT = - ~ \mc---~/ (v 2 _ V2o) + ~2v2/4u2,

where ~ is the damping costant. The value of the classical damping constant is given by

8~2e2v~ _ 2.510-22v~ s -1 " (89) ~ - 3mc3

It follows that the elastic-scattering cross-section for a molecule is several orders of magnitude greater than that for free electrons. Namely

(90) amT ~- 1023 GT.


As we pointed out before, elastic scattering of CBR photons by molecules will not alter the spectrum of CBR, but it will smear out anisotropies at the relevant frequencies. If a variety of molecules existed for a wide range of red-shifts, the resonant frequencies are broadened into a continuum and CBR anisotropies are smeared out over a wide spectral region. Finally, matter perturbations containing molecules will have peculiar velocities: the corresponding elastic scattering is no more isotropic and secondary anisotropies may arise.

The molecules considered are H2, H +, LiH, LiH +, Hell +, HD, HD+: even if H2, H + and HD are the most abundant, their interactions with photons are small, due to the lack of dipole moment; moreover, the quadrupole coupling is not sufficient to provide interesting absorption. As a matter of fact, the dipole moment of HD is not exactly zero, but it is so small (10-4 to be considered as negligible).

The resonance cross-section has to be normalized on the linewidth and the optical depth z is

(91) z = S anmold/,

where

23A~5 v c d Z a -- 8~c AVD nmol = fJOObpec~mnvs(1 + Z) ~, dl =

H o(1 + Z ) 2 4 1 + ~ Z '

where the notations mean

a = cross-section;

2, v = transition wavelength and frequency;

5vD = Doppler broadening;

A~r = Einstein coefficients;

f2, ~Ob = total and baryon density relative to the critical one;

Pc = critical density; am = molecular abundance to H;

n . s = population of level with quantum numbers v, j.

The presence of CBR guarantees that the population of the levels follows the Boltzmann distribution, i.e.

(92) n v j = (2j + 1) exp [-- Bej ( j + 1 ) / T 0 (1 + Z)]

Z (23 + 1) exp [-- B e j ( j + 1)/T0 (1 + Z)] exp [-- vf] (1 -- exp I f ] ) ,

where f = - weh/KT0 (1 + Z) and Be, We are rotational and vibrational constants. Due to the expansion of the Universe, a photon will change its frequency and

explore the entire linewidth of a given molecular resonance within a red-shift interval A Z = (1 + Z) �9 (Av/v) , if we neglect for a while the presence of perturbations (which could expand at different velocity with respect to the background).

The optical depth will depend on the molecule abundance and on the number of molecules in each quantum level considered as starting level in the process of elastic scattering. The optical depth for rotational and vibrational transitions is

8{} B. MELCHIORRI a n d F, MELCH[ORRI

102 !~ ',:~

T ~ ~ I ,-4 ,

101 f I I \ l i I I \ I

I I

- 1 ! I '1 . / - - - - . . . . . . . . . . . . . . . 1 0 II X ] 'I - I I

io -2

, ,~\ ! " - , , ' /

i \ ' /

i // 1 0 I 4 i ~ I L - ~ [ ~

- 5 l ~ ,

0 100 200 300 400 v(GHz)

Fig. 54. - Optical path due to molecules formed between Z= 1000 and Z= 70 under three different hypotheses about Li abundance (10 -s, 10 -9, 10 -~~ of H). The three frequencies of COBE DMR are also shown, in order to underline the possible effect of molecular scattering on CBR anisotropies. (Adapted from [146l). - - - Inhomogenous nucleosynthesis, - - Population II lithium abundance, - - - - - - Standard nucleosynthesis.

500 50 5 a r c r n i n - 8 i i I ] i i ~ i , , i I i ~ , i t ,,-.,

a) 100 GHz / ",,,

31.5 GHz

�9

0 4 810 40 100 400 1000L

e,1 _

-12

500 50 5 arcmin

b)

300 GHz

�9

] i I I I ~ i I i i i b r , i i i J

0 4 810 40 100 400 1000L

Fig. 55. - Erasing of primary CBR anisotropies due to elastic molecular scattering in the case of two different Li abundances: a) I0 -7, b) 6.10 -I~ as predicted by inhomogeneous and homogeneous nucleosynthesis[146]. Zj= 200, Z~ = 5.

shown in fig. 54. In fig. 55 the effect on CBR aniso t ropies is ske tchy i l lustrated, whi le in fig. 56 we have plot ted the s p e c t r u m of a typical pr imord ia l cloud.

Therefore , the p r e s e n c e of m o l e c u l a r sca t te r ing imply the following consequences :


10 -5

10 -6

IO

I0 -s

J I - - ' i

0 100 200 v(GHz)

Fig. 56. - Spectrum of a primordial molecular cloud at Z-- 200: the rotovibrational and vibrational lines are those of LiH and LiH +. Search for these clouds is in progress at IRAM [146].

1) CBR spectrum is unchanged,

2) small-scale anisotropies are erased (partially or totally) in a wavelength-dependent way, the effect being larger at longer wavelenghts.

In a word, we expect a different power index for CBR anisotropies in the millimetric and in the centimetric region. We should stress that the actual abundance of molecules is unknown and the effect could well be larger or smaller. In any case, the possible presence of molecular scattering has to be taken into consideration in planning new space experiments, because the choice of low frequencies (i.e. radioreceiver) coutd turn out to be unsatisfactory.

5"4. Exper imental problems in observing CBR anisotropies. - In table IV we have quoted the major characteristics of several recent experiments on CBR anisotropies: the typical experimental set-ups employed to search for CBR anisotropies range from conventional IR telescopes, where the secondary mirror of a Cassegrain system is wobbled in order to explore two regions few arcminutes apart in the sky: to the large, fiat wobbling mirror of Florence-Rome experiments, capable of extending the modulation amplitude up to several degrees in the sky: to the ,,sky-vs.-references~ system adopted by MIT: to the two-horn system of COBE-DMR; to the off-axis paraboloidal mirror of MAX experiment. Each configuration has its own merits and drawbacks. Before discussing them, it is better to list and briefly discuss the possible sources of spurious signals.

88

TABLE IV. --

B. MELCHIORRI a n d F. MELCHIORRI

Logo a n d

PI (~)

3000 m

BAM

H a l p e r n

40 k m

}~(mm) v ( G H z ) o ( c m -~) a 4} NET A~t Av At) ( b e a m - t h r o w ) ( m K / H z ~

1.2 250 8 12"-21"

0.2 42 2 a r c s e c

s in - s

I n t e r f e r o m e t e r 2 - 1 0 c m - ~ 1~ ~

1 c m -1 of r e so l u t i on sq-s

60

0.3

sky r eg ion A T / T r .....

( deg ree s )

10 '" 10' 1.8 " 1 0 - 4 ul

to be 3 " 10 -6

dec ided e x p e c t e d

MAX 1.7 180 6 0 .5~ ~ 0 .5 -0 .7

R i c h a r d s 0.2 20 0.6 s in - s

40 k m 1.1 270 9

0.1 30 1

0.8 375 12

0.1 40 1

UCSB HEMT 2 5 - 3 5 GHz 1.5~ ~ 0.7

L u b i n 2.5 GHz re so lu t ion s i n - s

S o u t h Pole

MSAM four c h a n n e l s at: 28 ' -0 .7 ~ 0.7

Meyer 5 . 6 - 8 . 7 - 1 5 . 8 - 2 2 . 5 c m - 1 sq-s

40 k m 1 . 8 - 1 . 1 - 0 . 6 3 - 0 . 4 4 m m

10% b a n d w i d t h

10 ~ �9 3 ~ 1.6 " 10 -5 4.7 �9 10 -5 d

n l

| 2 ~ 14 ~ 1.6 �9 10 -5 d l

0 . 8 - 1 0 -5 u l ]

n2 I circ le 8 ~ off 1 . 0 - 1 0 . 5

f r om Pole e x p e c t e d

MIT As above b u t for t he 3.8 ~ v s

Meyer 1.8 m m c h a n n e l a lone i n t e r n a l 40 k m r e f e r e n c e

0.6 30% of 4 .0 - 1 0 - 5 u l

t h e sky stat . ev idence

ULISSE 2 - 0 . 6 150 -500 5 - 1 7 3~ ~

Melch ior r i 0 .2 -0 .5 6 0 0 - 1 5 0 0 5 0 - 2 0 s in - s

40 k m 5 f l ights 5 - 8 c h a n n e l s

0.5 40% of 2 .0"10 -5 d

t he sky 1 .2 -10 -6 ul

ARGO 2 - 8 - 1 2 - 2 0 c m -1 0.50-1 ~

de B e r n a r d i s 10% b a n d w d t h s in-s

40 k m

0.5

TENERIFE 1 0 . 5 - 1 5 - 3 3 GHz 5.70-8 ~ ???

Davies s in -d

2000 m

3 ~ ~ 2 . 0 " 1 0 -5 d

6 ~ - 1000 2 -3" 10 -5 d

VLA 8.44 GHz 10-200"

Pa r t r idge 50 MHz b a n d w i d t h i n t e r f e r o m e t e r

i g r o u n d

100 �9 200 3 - 10 -5 ul

a r c sec at 22"

Note t ha t t h e g r o u n d m e a s u r e m e n t s a re w i t h i n bo ldface boxes . ( a ) PI = P r i n c i p a l Invest igator .


We may classify the possible sources of problems into:

i) instrumental and local enviromental effects (several ambient temperature sources are observed via diffraction and spurious reflections, like warm-optics emission, Earth's radiation, etc.);

ii) atmospheric disturbances (fluctuations at various angular scales);

iii) Solar System disturbances (Moon, Sun and planets observed directly or via diffraction and /o r reflection; zodiacal dust emission);

iv) galactic disturbances (galactic dust emission, sinchrotron emission, free-free emission).

Each research group has its own recipe to overcome (at least partially) the above problems.

Generally speaking, one has to worry for two kinds of spurious signals: those increasing the overall noise of the system and those simulating a true CBR anisotropy. The last ones are obviously the most dangereous, because they mimic what we are searching for. These signals should have properties similar to those expected for CBR anisotropies: this practically means that the time-scale of these signals should be longer than the observing time (usually, at least several minutes for pixel): atmospheric fluctuations at much shorter time-scales are easily recognized, although they increase the noise of the system. Slow changing instrumental offsets fall in this category of dangerous signals and one should avoid them in designing the experiment. For instance, when a ground-based telescope is following a celestial source, the sidelobes of its diffraction pattern explore different environmental zones, thereby determining a slowly changing offset in the detector output. As a second example, we may recall that in a balloon-borne experiment gondola oscillations combined with residual atmospheric emission would produce signals due to the modulation no more parallel to the horizon. These are huge effects, which may be alleviated by an appropriate strategy of observation. For instance, ground-based observations are carried out in the so-called s o u r c e t r a n s i t

configuration: the telescope is at rest and the zone to be explored moves across the field of view due to the Earth's rotation. Then the telescope is moved to a new position and the transit is repeated as many times as needed. One should keep in mind that this simple solution is in fact more complicated than it appears. The modulation across the sky has to remain parallel to the horizon: it follows (unless you are operating at the Poles) that the sky path of the wobbling beam is different for source transit at different elevations: therefore the signals cannot be simply added together and averaged. At balloon altitude the situation becomes worse: pointing is usually achieved by operating corrections through a system of motors and inertial wheels. It is not a surprise that oscillations up to several arcminutes are induced in this way. Even a slow continuous rotation of the gondola may have huge zenith oscillations, as in the case of MIT experiment [136], where the typical amplitude was of 0.4 ~ thereby inducing offset fluctuations as large as ~ 1 mK in the long-wave channel. The Rome-Florence Group has concluded that the best strategy is that of roughly pointing the region of interst and then turning the pointing motors off and leave the gondola free: after few minutes the zenith oscillations are damped down to a few arcseconds.

90 B. MELCtlIORRI and F. MELCHIORRI

Apart from these local effects, one has to worry for tile patchy distribution of galactic sources, like hot gas and dust, which produce significant signals in the radio and millimetric region. We may conclude that CBR anisotropies are affected by several spurious signals and the tendence of the various scientists is that of finding the best operating conditions, i.e. those capable of minimizing the disturbances. The usual free parameter employed in these analyses is the operating wavelength. Figure 57 shows the various local and galactic contributions as a function of the wavelength. This plot is rather misleading, however. One is not interested in the uniform component of the background, but in the spatial fluctuations of it. Therefore, it is impossible to select the best operating wavelength without taking into account the angular response, i.e. the transfer function of the istrument. For example, fluctuations in dust emission and in atmospheric emission usually increase with the angular diameter, while fluctuations due to radiogalaxies decrease with it. It follows that the power-spectrum diagram of anisotropies, as shown in fig. 53, has to be implemented with a similar diagram for the spurious contributions at various wavelengths of operation. This is schemati- cally shown in fig. 58. Two possible unknown sources of disturbances have to be added, however; very cold dust emitting in the far infrared may have a distribution different from that of warm dust; primordial molecules may erase CBR aniso- tropics in the radio region and produce secondary anisotropies at small angular scales. It follows that a complete characterization of CBR anisotropies would require detailed observations all over the spectrum.

wavelength (mm) 101 10 o 10 -1

/ ' ~ , S. Pole

m atmosphere .g - ~ -" \ ISD

i0_13 .-'"" \ ,

10-15 t """ "'" "" ~ i

-"" /'" synchrotron '\ i 0 - 1 7 - . . . . ~ - . . . . . . ,,,

10 ~ 101 102 frequency (cm -1)

Fig. 57. - Various sources of spurious signals compared with CBR. The brightness level corresponding to AT~T= 10 -6 is indicated by the dashed curve. The atmosphere at balloon altitude is more than three orders of magnitude more emissive, synchroton dominates at wavelengths longer than 5 mm, while dust (ISD) is important for wavelengths shorter than 3 mm. One has to take into account, however, that the curve for A T / T refers to anisotropies, while the other curves are relative to diffuse backgrounds (see next fig. 58).


10 - s

10 -9

r2

+

~ - 1 0

~ 10

-D_ 10

-12 10

vo ids g r e a t a t t r a c t o r r s u p e r c l u s t e r s c l u s t e r s

102 101 10 ~ Mpc l I i

90 ~ 2 ~ 10' 1" a n g u l a r s ca l e

101 102 1 0 3 10 4

l ( w a v e n u m b e r )

Fig. 58. - Power spectrum of anisotropies, as in fig. 53 but with the possible causes of spurious signals added. The power spectrum of galactic dust is derived from IRAS data and normalized to the values found by MAX, ULISSE and ARGO experiments. The power spectrum of atmosphere at balloon altitude has been derived by the few available data from MIT and Florence-Rome experiments at large angular scales, t] 0 ~- 1, Zls = 1000, n-= 1, a)-d): ~Jb=0 .2"0 .03 , H----50; e), f ) : •b ---- 0.05 -- 0.02, H---100 normalized at AT~T= 30 pK at angular scale of 10~ g) represents the gravitational waves.

55. Measurements of CBR anisotropies. - Few groups have detected CBR anisotropies, while many others have obtained upper limits only. Among these groups, two of them, namely COBE [200] and MIT [198, 199], have shown statistical evidence for anisotropies, but the sensitivity of their observations is not enough to allow an identification of the sky regions with positive or negative temperature excesses with respect to the mean. Therefore, the maps produced by these groups (and in the case of COBE published by several newspapers) are meaningless, because all the pixels are embedded in the detector noise. Statistical evidence for CBR anisotropies may be achieved in two ways. The first one consists in observing the same sky region with two identical receivers so that the sum of the two signals is proportional to the CBR anisotropies plus detector noise, while the difference of the two signals is proportional to the detector noise alone. Another way to obtain the evidence is that of computing the cross-correlation function of the data

(93) CM(") = ( A T ( O ) A T ( O + ~) )

after the removal of dipole and quadrupole anisotropies. This computation can be


carried out by using two channels, for instance the 53 GHz and 90 GHz of COBE or 170 GHz vs. COBE map in MIT experiment. Relation (93) is essentially a two-point correlation function and for large angular scales inflationary cosmolo- gies predicts a behaviour like [195-197]

6 Q2 ~ ( 2 / + 1) (94) C M ( ~ ) = ~ ~ l ( ~ WtP~(O, ~),

l=(~u~,~ ( + 1)

where Wz = exp [ - 1 / 2 (l + 1/2)~a 2] is the angular response ad Pt is the Leg- endre polynomial.

In such a kind of analysis one has to worry for the angular response of the system, which may mask the real CBR correlation if not correctly measured.

Three other groups, namely MAX (Berkeley), Tenerife (Cambridge) and ARGO-ULISSE (Rome) have detected CBR anisotropies with a 3a or more signal- to-noise ratio. This has been obtained by concentrating the efforts toward small sky regions, in order to improve the signal-to-noise ratio. The problem remains if the observed signals are due to CBR or to a residual dust emission, at least in the cases of MAX and ARGO experiments, while free-free and sinchrotron are the most plausible alternatives in the case of Tenerife experiment. It is unfortunate that different sky regions have been observed by the three experiments so that not a single region of the sky is at present measured in all t he CBR spectrum. The observed sky regions are shown in fig. 59, and some of the observed signals are drawn in fig. 60.

Generally speaking, there is a trend: small-scale, radio observations seem to indicate lower values of CBR fluctuations than large scale and /o r millimetric observations. Three possible scenarios follow:

8O 90

40

30

20

o

Fig. 59. - Sky regions explored by experiments which claimed CBR anisotropy detection at intermediate angular scales (10' up to 10 degrees).

THE COSMIC BACKGROUND RADIATION

a) 5

§

x ~

north galactic spur I ~ I I I I I I I I I I I I I I I ~ I

4

~ o

0 2 0 4 0 6 0 8 0 b ) a z i m u t h ( d e g r e e s )

' I . . . . I ' ~ ' ' I ' 'A

500~- ~ ~ '

~ 0 <1 - 2 5 ~

-5oo~-

500L ' ' I . . . . ' ' ' ~ ' ' ' 'C ~

~ ~o~- ~ . _ ~ ~ AI~

, ~ 200

lOOV ~ . . . . . , , , , , , , , :~

- i ~-, , , . . . . ~ . . . . ~ , , ,~ 150 200 25O right ascension (degrees)

c)

lOO . . . . . . . . . . . . . .

50 ~ �9 T/~ \

-50 hann -I~176 ~ , 1 ~ .... re . . . . . . .

loo~

~ -50 | _100 c~ u cm cnannei

lOOL ~o~

-5o~ _ ,

12 cm channel -looL . . . . . . . . . . . . . . . . .

224 227 230 233 236 239 242 right ascension (degrees), epoch 1991

"~ ~ d)

-~,~ 0.0F.+ +* . . . . . . %++ +~+ . . . . . . ~ +

d -o .shi :~ % 4 0 0 0 ~ - . . . . I ' ~ E ' ' [ . . . . I

F4OOOL:_ ~f _ ~ _ _

<1 1 0 0 ' ' ~ I I ' ~ ' ' I ' ' ' ' I

~<; -~ok< 7 , , ,~,, ?~,~,, ~, T 0 2 0 4 0 6 0

f i e l d n u m b e r

93

<IO

<I,-~

Fig. 60. - Signals quoted as CBR anisotropies detection: a) observations of Florence- Rome group in 1980; b) ULISSE upper limits in 1985-1989; c) MAX detection in 1992-93; d) ARGO detection in 1993. See table IV for experimental details.

a) The differences between large scale and in termedia te scale are real, while mill imetric and radio observations have similar ampli tudes: the small-scale defect in anisotropy may be explained as a late reionizat ion or as due to the p resence of gravitational waves, which increases large-scale per turbat ions.

b) The differences between mill imetric and radio observations are real: they may be explained with the p resence of pr imordia l molecules of LiH which scat tered more efficiently radio waves, or as due to an infrared excess in dust emission, both from our Galaxy or in the intergalactic medium.


c) There are no differences in anisotropies at various wavelengths and larger-than-horizon anisotropies have a flat spectrum: inflation is confirmed and some sort of CDM cosmology will fit the data.

The possibility of distinguishing among these scenarios is discussed in the following subsection.

5"6. F u t u r e p l a n s : w h a t CBR a n i s o t r o p i e s c a n te l l u s a n d w h a t t h e y can - not. - It is hard to decide if signals observed by COBE and other groups are CBR anisotropies or a mixture of CBR and spurious signals: in the first case, their knowledge will provide a picture of the last scattering surface for angular scales greater than 10 arcmin: at smaller angular scales the optical thickness of LSS is large enough to average and erase the anisotropies along the line of sight.

Therefore, what the study of CBR is providing at best is a bidimensional map of perturbations with comoving dimensions larger than those of superclusters today. Referring to fig. 53 it follows that a suppression of angular scales smaller than 5 arcmin (superclusters) would substantially live the amplitude of the observed CBR anisotropies unchanged: a Universe withouth galaxies would produce the same anisotropies of the observed one! Vice versa, if we suppress all the large-scale fluctuations, so that CBR anisotropies became undetectable, the apparent distribution of galaxies would substantially remain unchanged; i.e. the observed nearby Universe could exist even with CBR anisotropies equal to zero. Still, cosmologists pretend to reconstruct the process of galaxy formation from the analysis of this map. First of all, it implies that the power spectrum of perturbations has a single slope from superclusters to galaxies, so that the study of the large perturbations on LSS may allow to predict the behaviour of the smaller one. The second point relies on the application of methods of analysis which have already failed in the study of galaxy distribution: the two-point correlation function, when employed in galaxy statistics, was unable to evidentiate important effects, like huge voids or matter concentrations. Why do we have to believe that in the case of CBR this algorithm will provide a more efficient method?

The third point is that molecules, dust and gas may affect in several ways CBR photons along their travel from LSS to us. Primary anisotropies may be partially or totally erased in a wavelength-dependent way as well as in a different amount depending on the angular scale. Secondary anisotropies may appear at small and intermediate angular scales.

This being the situation, it is hard to believe that rapid progresses in Cosmology can be obtained, unless a wide systematic programme of research is organized. In this programme, future measurements of CBR anisotropies may or may not play a relevant role, depending on the trasparency of the Universe. Several satellite and balloon programmes have been proposed to measure CBR anisotropies at 0.5-5 degrees: it is unfortunate that this interesting research programme is apparently not complemented with what should be the natural evolution of observational Cosmology, i.e. the study of the Universe at i000 > Z > 5.

But let us analyse the situation in more detail. In our opinion the first most important problem to be solved is that of the physical mechanism responsible for galaxy formation. Roughly speaking, two alternatives are still passing the observational tests: the linear theory of gravitational instability and the highly non-linear theory of matter condensation in the potential wells of topological defects, like cosmic strings. The last hypothesis is considered by some authors as a

TIIE COSMIC BM~KGROUND RADIATION 95

bit too odd to be taken seriously: one should remember, however, that nobody has observed the hot or cold non-baryonic matter required by the first hypothesis! Brandenbergher [203] has clearly shown that the two hypotheses are in agreement with the observed levels of anisotropy. Cosmic strings predict, however, a significantly non-Oaussian distribution at small angular scales. Dedicated telescopes and special topological analysis are needed to solve the problem. It is unfortunate that all the proposed space experiments have not enough angular resolution to provide useful information. Recently, Pompilio [204] has shown that a resoMng power of 5 arcmin could be adequate if one employs the powerful method of multifractal analysis. This means that even a three-meter telescope operating in the millimetric region would be adequate. The only available telescope is that of TIR Project, which, however, is at present in stand-by, due to an unfortunate decision of the Italian Space Agency. FIRST, the European millimetrie space telescope, could provide important information, if bolometers were allowed.

Once this problem is solved, if the theory of gravitational instability would prevail, the next important point will be that of deciding the role of tensor f luc tua t ions , i.e. of primordial gravitational waves. The amount of these perturbations is linked to tile specific nature of the inflation (see Davis [205], for a review of the subject). As shown in figure 58, this problem may be solved by a comparison between the amplitude of anisotropies at large (quadrupole) and intermediate (2-5 degrees) angular scales, in order to cheek whether the long-wave power spectrum is flat or not. COBE has provided a very limited amount of information in this respect, just because the error bars are too large. The only planned space experiment in this angular range is RELIC 2. Some other proposed experiments, like SAMBA would explore the intermediate-scale range, but a decision about GW (gravitational waves) contribution would require a new more precise measurement of the large-scale anisotropy.

The next problem to be solved is that of a possible reionization: the lack of a significant increase of anisotropies for angular scales smaller than the horizon at decoupling (_< 2-5 degrees) would be a definite test of this fact. A wide range of experiments (balloon-satellite) are in the position to answer this question. One should note, however, that the presence of a significant reionization would render CBR anisotropies observations at small angular scales impossible. Among the various proposed space experiments, only SAMBA has taken seriously into consideration this possibility, by including in the programme a search for the SZ effect on the ionized protoclouds, characterized by the typical spectral signature of the SZ effect. Also, ground-based observations of secondary anisotropies, like the VLBI searches could help in understanding the structure of the primordial Universe.

If reionization turned out to be negligible, one has still to worry for molecular scattering: a comparison of CBR anisotropies at the same small angular scale but in the radio and millimetric regions would fix this question: it could also heIp in measuring the primordial abundance of Li. Search for secondary anisotropies by means of ground-based telescopes and by FIRST could open the new field of cosmological spectroscopy.

In conclusion, the most promising results are expected to come from a combi- nation of submillimetric and radio observations of CBR anisotropies at small angular scales: confirmations of COBE results are needed, however, at a much better level of sensitivity.


R E F E R E N C E S

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the cosmic background radiation

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