Jim Peebles and the Nascence of Physical Cosmology

福來正孝

Institute for Advanced Study, Princeton

16 March 2020

Chronicle of Cosmology — pre war period

1915/6 Einstein: General Relativity

1917 Einstein: GR applies to understanding the Universe

1922 Friedman: Cosmological solution: ODE

1927 : Distance-Velocity relation (“Hubble law”)

+ identified as the expansion in Einstein eq.

1929 Hubble: Distance-Velocity relation = Hubble law

Lemaitre

Rµ� �12gµ�R� �gµ� = �8�GTµ�

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post war till 1965

Gamow 1946 + (Alpher, Herman 1948-1950)

extrapolate expansion to t=0: hot Big Bang

Lifshitz 1946 perturbation theory in expanding Universe

Hayashi 1950 beta equilibrium: (p,n) abundances

Peebles 1965; Dicke, Peebles, Roll, Wilkinson 1965

Penzias, Wilson 1965 (13 V 1965)

(8 III 1965) (7 V 1965)prediction of CMBCMB discovered!

Peebles 1968 generation of black-body radiation

ca 1968

390 citations

390 citations(164 to 1980)

177 citations(97 to 1980)

see: Dicke, Behringer, Kyhl, Vene 1946

Dicke, Behringer, Kyhl, Vene 1946 H.Tanaka, Kakinuma, Sindo, Takayanagi 1953 Crawford, Hogg, Hunt (Bell Lab) 1961 �T = 3.5K

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T < 5K

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T < 20K

<latexit sha1_base64="VK6eVwm85b5UXAwvgr9gnUNNTa0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyGiB48BL0IXiLkBckSZiezyZCZ2WVmVohL8Fe85KCIV//Dm3/j5HHQxIKGoqqb7q4g5kwb1/12MmvrG5tb2e3czu7e/kH+8Kiho0QRWicRj1QrwJpyJmndMMNpK1YUi4DTZjC8nfrNR6o0i2TNjGLqC9yXLGQEGysNoQbXUAIXUpiAAgEI7mHczRfcojsDWiXeghRggWo3/9XpRSQRVBrCsdZtz42Nn2JlGOF0nOskmsaYDHGfti2VWFDtp7Prx+jMKj0URsqWNGim/p5IsdB6JALbKbAZ6GVvKv7ntRMTXvkpk3FiqCTzRWHCkYnQNArUY4oSw0eWYKKYvRWRAVaYGBtYzobgLb+8ShqlolcuXjyUC5WbRRxZOIFTOAcPLqECd1CFOhB4ghd4hTfn2Zk4787HvDXjLGaO4Q+czx88qJE8</latexit>

Legacy of war efforts:advanced microwave technology! 1. Lamb shift 2. exploring microwave sky

Discovery of CMB: Great epoch for physical cosmology Penzias-Wilson & Peebles

see:

Shane-Wirtanen (Seldner) sky 1967

statistic introduced: two point correlation function ⇠(r) = h⇢(x+ r)⇢(x)i

<latexit sha1_base64="qsVieOxuhafAxR+b+/RmbCQ/og0=">AAACNXicbVDLSgMxFL1TX7W+Rl26CRZFEcqMVHQjFN24rGAf0JaSSdM2NJMMSUZaSj/HH3Djf7jShQtF3PoLpg+ktl4IOfecc0nuCSLOtPG8VyexsLi0vJJcTa2tb2xuuds7RS1jRWiBSC5VOcCaciZowTDDaTlSFIcBp6Wgcz3US/dUaSbFnelFtBbilmBNRrCxlHQP4QG6wOAIFBzDpe04YBDQsjcFZHsFbZBW78LJyDPNjLtff91NexlvVGge+BOQhknl6+5ztSFJHFJhCMdaV3wvMrU+VoYRTgepaqxphEkHt2jFQoFDqmv90dYDdGCZBmpKZY8waMROT/RxqHUvDKwzxKatZ7Uh+Z9WiU3zotZnIooNFWT8UDPmyEg0jBA1mKLE8J4FmChm/4pIGytMjA06ZUPwZ1eeB8XTjJ/NnN1m07mrSRxJ2IN9G6sP55CDG8hDAQg8wgu8w4fz5Lw5n87X2JpwJjO78Kec7x8u3558</latexit>

2D projection : w(✓)

<latexit sha1_base64="umkFyD3tUsRkT7U04Ab2O6G8ho0=">AAACJXicbVBNSwMxEJ31s9avqkdBgkXQS9kVRfEk6sGjgm2FWiSbpjaaTZZkVilFf4wg/hUvHiwiePKvOK09+DUQ5vHeGybz4lQrj2H4HgwNj4yOjecm8pNT0zOzhbn5ireZE7IsrLbuNOZeamVkGRVqeZo6yZNYy2p8td/Tq9fSeWXNCbZTWU/4hVFNJTgSZQtLsA4HcAcMHsBBQj2lbuESJAhAUIQN7JDjDm5glVwILdIQOKydF4phKewX+wuiASjCoI7OC92zhhVZIg0Kzb2vRWGK9Q53qISWt/mzzMuUiyt+IWsEDU+kr3f6V96yFWIarGkdPYOsz36f6PDE+3YSkzPh2PK/tR75n1bLsLld7yiTZiiN+FrUzDRDy3qRsYZyUqBuE+DCKforEy3uuEAKNk8hRL9P/gsq66Voo7R5vFHc3RvEkYNFWKZII9iCXTiEIyhT5PfwBC/QDR6D5+A1ePuyDgWDmQX4UcHHJybBmqs=</latexit>

CMB fluctuations - cosmic structure connexion: Sunyaev Zeldovich 1970 Peebles Yu 1970

Statistical distribution of galaxies Peebles 1973 -

w/ Ed Groth, Jim Fly, Mike Seldner, Mark Davis, …

Infinite amount of work created!

2D ! 3D

<latexit sha1_base64="j4+B6gRd/pM12rK6JEyuF8kcbjs=">AAACDXicbZC7TgJBFIbP4g3xtmJps5GYWJFdxGhJlMISE7kksCGzwyxMmN3ZzMxqyAYewMansLex0BhbezvfxgG2UPBPJvnyn3Ny5vxexKhUtv1tZFZW19Y3spu5re2d3T1zP9+QPBaY1DFnXLQ8JAmjIakrqhhpRYKgwGOk6Q2vpvXmHRGS8vBWjSLiBqgfUp9ipLTFzTyUoAoTeAIBFPowAAVIswAO99qfwClUu2bBLtozWcvgpFCAVLWu+dXpcRwHJFSYISnbjh0pN0FCUczIONeJJYkQHqI+aWsMUUCkm8yuGVvH2ulZPhf6hcqaub8nEhRIOQo83RkgNZCLtan5X60dK//CTWgYxYqEeL7Ij5mluDWNxupRQbBiIw0IC6r/auEBEggrHWBOh+AsnrwMjVLRKRfPbsqFymUaRxYO4QhOwIFzqMA11KAOGB7gGV7hzXg0Xox342PemjHSmQP4I+PzB1UslW4=</latexit>

⇠(r) = h⇢(x+ r)⇢(x)i

<latexit sha1_base64="qsVieOxuhafAxR+b+/RmbCQ/og0=">AAACNXicbVDLSgMxFL1TX7W+Rl26CRZFEcqMVHQjFN24rGAf0JaSSdM2NJMMSUZaSj/HH3Djf7jShQtF3PoLpg+ktl4IOfecc0nuCSLOtPG8VyexsLi0vJJcTa2tb2xuuds7RS1jRWiBSC5VOcCaciZowTDDaTlSFIcBp6Wgcz3US/dUaSbFnelFtBbilmBNRrCxlHQP4QG6wOAIFBzDpe04YBDQsjcFZHsFbZBW78LJyDPNjLtff91NexlvVGge+BOQhknl6+5ztSFJHFJhCMdaV3wvMrU+VoYRTgepaqxphEkHt2jFQoFDqmv90dYDdGCZBmpKZY8waMROT/RxqHUvDKwzxKatZ7Uh+Z9WiU3zotZnIooNFWT8UDPmyEg0jBA1mKLE8J4FmChm/4pIGytMjA06ZUPwZ1eeB8XTjJ/NnN1m07mrSRxJ2IN9G6sP55CDG8hDAQg8wgu8w4fz5Lw5n87X2JpwJjO78Kec7x8u3558</latexit>

w(✓) ⇠Z

⇠(x)dz

<latexit sha1_base64="G+oDicjRG/rsd8f8oNqu+EiBXoM=">AAACIXicbZBLTwIxEMdn8YX4Qj3qoZGYwIXsGoweiV48YiKPBAnplgIN3e6m7apI+CpejN/EiweN4Wb8Mg6Pg4KTtPnNf2bSzt+PpDDWdb+cxNLyyupacj21sbm1vZPe3auYMNaMl1koQ13zqeFSKF62wkpeizSngS951e9djuvVO66NCNWN7Ue8EdCOEm3BqEUpTB/CPWThBSx0geNNIYeZAQEBECQBCtUxPSBn8c5h1oLHZjrj5t1JkEXwZpCBWZSa6dFtK2RxwJVlkhpT99zINgZUW8EkH6ZuY8Mjynq0w+uIigbcNAaTDYfkGJUWaYcaj7Jkov6eGNDAmH7gY2dAbdfM18bif7V6bNvnjYFQUWy5YtOH2rEkNiRju0hLaM6s7CNQpgX+lbAu1ZRZNDWFJnjzKy9C5STvFfKn14VM8WJmRxIO4Ajt9OAMinAFJSgDgyd4hXf4cJ6dN+fTGU1bE85sZh/+hPP9A1nfmcU=</latexit>

�T/T vs �⇢/⇢

<latexit sha1_base64="k4gODH/aCeeRXOYJU/LZ0mbsBbM=">AAACM3icbVDLSgMxFL3js9bXqEs3wVJwVWekosuiLlxW6AvaUjJp2oZmJkOSKZSh/o17N/6IC0FcKOLWfzDTzqK23nDhcM653NzjhZwp7Thv1srq2vrGZmYru72zu7dvHxzWlIgkoVUiuJANDyvKWUCrmmlOG6Gk2Pc4rXvDm0Svj6hUTAQVPQ5p28f9gPUYwdpQws7DI9wCBQ4aMCCowJnpB/Nio0jwDTcCBZMpN+9N1AEI409Rx845BWdaaBm4KchBWuWO/dLqChL5NNCEY6WarhPqdoylZoTTSbYVKRpiMsR92jQwwD5V7Xh68wTlDdNFPSFNBxpN2fmJGPtKjX3POH2sB2pRS8j/tGake1ftmAVhpGlAZot6EUdaoCRA1GWSEs3HBmAimfkrIgMsMdEm5qwJwV08eRnUzgtusXBxX8yVrtM4MnAMJ3AKLlxCCe6gDFUg8ASv8AGf1rP1bn1Z3zPripXOHMGfsn5+AfPLnx8=</latexit>

1992 COBE DMR brought us a very good news that we are on the right track: gravitational instability theory is correct but amplitudes are too small by 100 times

COBE DMR temp. fluctuation

convincing evidence for ‘dark matter’

�T/T ⇠ 10�5

<latexit sha1_base64="RPNNqc9vrDx4ByGmr7ppfofeZXI=">AAACF3icbZC7SgNBFIbPxluMt1ULC5vBINgYdyVBy6AWlhFyg2QNs5NJMmR2Z5mZFcKSt7DxAXwJGwtFbLXzbZwkW2j0hwMf/zmHmfP7EWdKO86XlVlYXFpeya7m1tY3Nrfs7Z26ErEktEYEF7LpY0U5C2lNM81pM5IUBz6nDX94Oek37qhUTIRVPYqoF+B+yHqMYG0sYe/BI1wBBQ4aMCCowokpZFwFDAJDLjhwCwkcQwnGHTvvFJyp0F9wU8hDqkrH/mx3BYkDGmrCsVIt14m0l2CpGeF0nGvHikaYDHGftgyGOKDKS6Z3jdGhcbqoJ6SpUKOp+3MjwYFSo8A3kwHWAzXfm5j/9Vqx7p17CQujWNOQzB7qxRxpgSYhoS6TlGg+MoCJZOaviAywxESbKHMmBHf+5L9QPy24xULpppgvX6RxZGEfDuDIRHoGZbiGCtSAwD08wQu8Wg/Ws/Vmvc9GM1a6swu/ZH18A6+MlkU=</latexit>

Dark matter massive neutrinos: Cowsik, McClelland 1972 heavier neutrinos: May-June 1977: Hut, Lee-Weinberg, Sato-Kobayashi, Dicus-Kolb-Teplitz, Vysotskii et al. heavy hypothetical neutral particles = ‘cold dark matter’ Bond-Szalay-M.Turner 4 Dec 1981 Blumenthal-Pagels-Primack 5 Jan 1982 Peebles 2 July 1982

Pagels-Primack 17 Aug 1981� keV neutrinos

m� � 30eV

give a right characteristic mass for galaxies M � 1012M�

they give a proper perturbation spectrum

Era of simulations

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No. 1, 1982 SCALE-INVARIANT PRIMEVAL PERTURBATIONS L3 and the angular power spectrum of the background is

(a,)2 = 6(a2)2/[/(/+!)]. (14)

The 5-wave part a0 diverges, corresponding to the loga- rithmic divergence in the primeval spectrum P cc k. The /7-wave does not include the effect of our peculiar mo- tion.

The autocorrelation function of the background tem- perature after the /7-wave has been eliminated is (LSS §46)

HOn) = (TxT2)/(T)2 - 1

- S(«/)2(2/+^^(cos Í12)/4W. (15) /> 1

At 9U « 1 radian, this with equation (14) gives

w(0) = (3/”)allog(®/6), (16)

where © is on the order of the size of the field within which w(9) is measured.

d) Mass Fluctuations A convenient measure is the rms fluctuation in the

mass found within a randomly placed sphere of radius R. We have from equation (8)

SM/M =32 S*(sin kR - kRcos kR)/{kR)\

(17)

With equations (6) and (10), this gives the rms value

8M M

V(R)f=j k3 dk

0 (1+ 6k + 2.65k2)2

X (sin kR — kR cos kR )2

{kR)6 (18)

M/Mo I010 I012 I014 I016 I018

Fig. 1.—The rms fluctuation in the mass found within a sphere of radius R. The top scale is the mean mass within the sphere. The vertical normalization is adjusted to make 8M/M agree with the observed fluctuation, 8N/N, in the count of bright galaxies at R = 8 h~x Mpc. This curve is based on the assumptions that the universe is dominated by very massive, weakly interacting particles and that the initial density fluctuations were adiabatic with power spectrum P cc k.

pr > px. Shortward of the scale r fixed by mx (eq. [5]), the power spectrum is truncated by thermal motions so 8M/M is independent of R. At large R, 8M/M oc R~2, which is the primeval spectrum. At 1 < Æ < 30 Mpc, 8M/M varies roughly as R~125.

Figure 1 can be compared to the curve tz = 1 in Figure 2 of Bond, Szalay, and Turner (1982). The short- wavelength cutoff in the latter curve results from the assumption mx ~ 1 keV. The Bond et al. curve peaks at M ~ 1012 M0 as does the Jeans mass found by Blumenthal, Pagels, and Primack (1982), both of which agree with the position of the break in Figure 1. This is consistent with the fact that mx — 1 keV is roughly equivalent to the limit of very large mx.

By equations (18) and (19), the expected quadrupole moment of the microwave background is

a2 = 3.5 X 1(T6. (20)

Figure 1 shows 8M/M for h — t = \ and the normali- zation

-^-{R = 8 Mpc) = 1, (19)

which agrees with the rms fluctuation, 8N/N, in the counts of bright galaxies at R = S h~l Mpc (LSS § 59; Davis and Peebles 1983). At Æ<0.1 Mpc, 8M/M varies only slowly, as | log R |1/2, fluctuations with fixed variance per octave of R having been stored when

For the case of baryon-dominated matter, Silk and Wilson (1981) found û2 “ 4 X 10~5. The larger value is the result of the much broader mass coherence length, which increases the integral J3 — fr2 dr £ (Peebles 1981/7).

The Boughn, Cheng, and Wilkinson (1981) measure- ments imply 02 ~ 3 X 10-4, but the more recent mea- surements of Lubin (1982) and Fixsen (1982) suggest the extragalactic anisotropy may be appreciably less than that and hence perhaps not inconsistent with equation (20).

© American Astronomical Society • Provided by the NASA Astrophysics Data System

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The Astrophysical Journal, 263:L1-L5, 1982 December 1 © 1982. The American Astronomical Society. All rights reserved. Printed in U.S.A.

LARGE-SCALE BACKGROUND TEMPERATURE AND MASS FLUCTUATIONS DUE TO SCALE-INVARIANT PRIMEVAL PERTURBATIONS

P. J. E. Peebles Joseph Henry Laboratories, Physics Department, Princeton University

Received 1982 July 2; accepted 1982 August 13

ABSTRACT The large-scale anisotropy of the microwave background and the large-scale fluctuations in the

mass distribution are discussed under the assumptions that the universe is dominated by very massive, weakly interacting particles and that the primeval density fluctuations were adiabatic with the scale-invariant spectrum P oc wavenumber. This model yields a characteristic mass comparable to that of a large galaxy independent of the particle mass, mx, if mx > 1 keV. The expected background temperature fluctuations are well below present observational limits. Subject headings: cosmic background radiation — cosmology — galaxies: formation

I. INTRODUCTION It is useful to consider which scenarios for the nature

and evolution of the mass distribution in the universe can fit the observations without undue contrivance. We may hope that as the observations improve the list of candidates will narrow, and that this process may in time help guide us to a fundamental theory of the origin of structure in the universe. The picture discussed here is motivated by the argument that, if the initial conditions for conventional classical cosmology were set at some exceedingly high redshift (perhaps the Planck time or the grand unified theory epoch), and if the initial condi- tions did not involve exceedingly large or small num- bers, then the cosmological density parameter ought to be ß = 1, and, assuming adiabatic density perturba- tions, the power spectrum P ought to be proportional to the wavenumber k (e.g., Hawking 1982). Density fluctuations on scales greater than the horizon are de- fined as in Peebles (1980, § 91, hereafter LSS). If P cc perturbations to the geometry diverge only as log k so the cutoffs can be at very large and small k and the spectrum can be truly scale invariant (Harrison 1970; Peebles and Yu 1970, § Via; Zerdovich 1972). Density fluctuations appearing on the horizon have a fixed value, SM/M ~ 10-4, and, as this number is not greatly dif- ferent from unity, we might imagine it is fixed by fundamental physics.

Observational constraints include the measurements of background temperature fluctuations, ÔT/T < 1 X 10“4 (Boughn, Cheng, and Wilkinson 1981; Melchiorri et al. 1981) and the estimate of the coherence length of the galaxy distribution. They tell us P oc A: is unaccept- able in the usual cosmology with baryons, electrons, radiation, and massless neutrinos. The observations of 8T/T imply e < 1 X 10“4. The wanted growth factor

~ 104 to make nonlinear density fluctuations form by the present epoch is obtained if Û ~ 1 (Silk and Wilson 1981) because density fluctuations on scales greater than the matter-radiation Jeans length, \x, grow before de- coupling. However, Xx is large so it makes the mass autocorrelation function unacceptably broad (Silk and Wilson 1981; Peebles 1981a). Press and Vishniac (1980) emphasized that there is no hope for the development of appreciable density fluctuations on scales smaller than Ac-

The problem is relieved if the universe is dominated by massive, weakly interacting particles because density fluctuations on small scales can grow before decoupling. This effect has been widely discussed in the case that the weakly interacting particle mass, mx, is some tens of electron volts (e.g., Doroshkevich et al. 1981 and refer- ences therein). If ß ~ 1, the mass coherence length is broad but perhaps not unacceptable (Peebles 1982 a). The case mx — 1 keV is discussed by Bond, Szalay, and Turner (1982) and Blumenthal, Pagels, and Primack (1982). I discuss here a particularly simple and perhaps important limiting case, mx> \ keV. The main results are the spectrum of mass fluctuations, which seems quite reasonable for the production of galaxies and clusters of galaxies, the statistical character of the background tem- perature fluctuations, and the expected size of the mass density anticorrelation at large separations.

II. CALCULATION I assume zero cosmological constant and ß = 1, the

mass being mainly in weakly interacting particles, mass mx. Following Davis et al. (1981), I take the particle distribution in phase space at u « c in the absence of

LI

© American Astronomical Society • Provided by the NASA Astrophysics Data System

The WMAP satellite (2003) measurements found a2 = 5± 1⇥ 10�6

The CDM Cosmology

1982

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No. 1, 1982 SCALE-INVARIANT PRIMEVAL PERTURBATIONS L3 and the angular power spectrum of the background is

(a,)2 = 6(a2)2/[/(/+!)]. (14)

The 5-wave part a0 diverges, corresponding to the loga- rithmic divergence in the primeval spectrum P cc k. The /7-wave does not include the effect of our peculiar mo- tion.

The autocorrelation function of the background tem- perature after the /7-wave has been eliminated is (LSS §46)

HOn) = (TxT2)/(T)2 - 1

- S(«/)2(2/+^^(cos Í12)/4W. (15) /> 1

At 9U « 1 radian, this with equation (14) gives

w(0) = (3/”)allog(®/6), (16)

where © is on the order of the size of the field within which w(9) is measured.

d) Mass Fluctuations A convenient measure is the rms fluctuation in the

mass found within a randomly placed sphere of radius R. We have from equation (8)

SM/M =32 S*(sin kR - kRcos kR)/{kR)\

(17)

With equations (6) and (10), this gives the rms value

8M M

V(R)f=j k3 dk

0 (1+ 6k + 2.65k2)2

X (sin kR — kR cos kR )2

{kR)6 (18)

M/Mo I010 I012 I014 I016 I018

Fig. 1.—The rms fluctuation in the mass found within a sphere of radius R. The top scale is the mean mass within the sphere. The vertical normalization is adjusted to make 8M/M agree with the observed fluctuation, 8N/N, in the count of bright galaxies at R = 8 h~x Mpc. This curve is based on the assumptions that the universe is dominated by very massive, weakly interacting particles and that the initial density fluctuations were adiabatic with power spectrum P cc k.

pr > px. Shortward of the scale r fixed by mx (eq. [5]), the power spectrum is truncated by thermal motions so 8M/M is independent of R. At large R, 8M/M oc R~2, which is the primeval spectrum. At 1 < Æ < 30 Mpc, 8M/M varies roughly as R~125.

Figure 1 can be compared to the curve tz = 1 in Figure 2 of Bond, Szalay, and Turner (1982). The short- wavelength cutoff in the latter curve results from the assumption mx ~ 1 keV. The Bond et al. curve peaks at M ~ 1012 M0 as does the Jeans mass found by Blumenthal, Pagels, and Primack (1982), both of which agree with the position of the break in Figure 1. This is consistent with the fact that mx — 1 keV is roughly equivalent to the limit of very large mx.

By equations (18) and (19), the expected quadrupole moment of the microwave background is

a2 = 3.5 X 1(T6. (20)

Figure 1 shows 8M/M for h — t = \ and the normali- zation

-^-{R = 8 Mpc) = 1, (19)

which agrees with the rms fluctuation, 8N/N, in the counts of bright galaxies at R = S h~l Mpc (LSS § 59; Davis and Peebles 1983). At Æ<0.1 Mpc, 8M/M varies only slowly, as | log R |1/2, fluctuations with fixed variance per octave of R having been stored when

For the case of baryon-dominated matter, Silk and Wilson (1981) found û2 “ 4 X 10~5. The larger value is the result of the much broader mass coherence length, which increases the integral J3 — fr2 dr £ (Peebles 1981/7).

The Boughn, Cheng, and Wilkinson (1981) measure- ments imply 02 ~ 3 X 10-4, but the more recent mea- surements of Lubin (1982) and Fixsen (1982) suggest the extragalactic anisotropy may be appreciably less than that and hence perhaps not inconsistent with equation (20).

© American Astronomical Society • Provided by the NASA Astrophysics Data System

1982

ApJ

. . .2

63L.

. .IP

The Astrophysical Journal, 263:L1-L5, 1982 December 1 © 1982. The American Astronomical Society. All rights reserved. Printed in U.S.A.

LARGE-SCALE BACKGROUND TEMPERATURE AND MASS FLUCTUATIONS DUE TO SCALE-INVARIANT PRIMEVAL PERTURBATIONS

P. J. E. Peebles Joseph Henry Laboratories, Physics Department, Princeton University

Received 1982 July 2; accepted 1982 August 13

ABSTRACT The large-scale anisotropy of the microwave background and the large-scale fluctuations in the

mass distribution are discussed under the assumptions that the universe is dominated by very massive, weakly interacting particles and that the primeval density fluctuations were adiabatic with the scale-invariant spectrum P oc wavenumber. This model yields a characteristic mass comparable to that of a large galaxy independent of the particle mass, mx, if mx > 1 keV. The expected background temperature fluctuations are well below present observational limits. Subject headings: cosmic background radiation — cosmology — galaxies: formation

I. INTRODUCTION It is useful to consider which scenarios for the nature

and evolution of the mass distribution in the universe can fit the observations without undue contrivance. We may hope that as the observations improve the list of candidates will narrow, and that this process may in time help guide us to a fundamental theory of the origin of structure in the universe. The picture discussed here is motivated by the argument that, if the initial conditions for conventional classical cosmology were set at some exceedingly high redshift (perhaps the Planck time or the grand unified theory epoch), and if the initial condi- tions did not involve exceedingly large or small num- bers, then the cosmological density parameter ought to be ß = 1, and, assuming adiabatic density perturba- tions, the power spectrum P ought to be proportional to the wavenumber k (e.g., Hawking 1982). Density fluctuations on scales greater than the horizon are de- fined as in Peebles (1980, § 91, hereafter LSS). If P cc perturbations to the geometry diverge only as log k so the cutoffs can be at very large and small k and the spectrum can be truly scale invariant (Harrison 1970; Peebles and Yu 1970, § Via; Zerdovich 1972). Density fluctuations appearing on the horizon have a fixed value, SM/M ~ 10-4, and, as this number is not greatly dif- ferent from unity, we might imagine it is fixed by fundamental physics.

Observational constraints include the measurements of background temperature fluctuations, ÔT/T < 1 X 10“4 (Boughn, Cheng, and Wilkinson 1981; Melchiorri et al. 1981) and the estimate of the coherence length of the galaxy distribution. They tell us P oc A: is unaccept- able in the usual cosmology with baryons, electrons, radiation, and massless neutrinos. The observations of 8T/T imply e < 1 X 10“4. The wanted growth factor

~ 104 to make nonlinear density fluctuations form by the present epoch is obtained if Û ~ 1 (Silk and Wilson 1981) because density fluctuations on scales greater than the matter-radiation Jeans length, \x, grow before de- coupling. However, Xx is large so it makes the mass autocorrelation function unacceptably broad (Silk and Wilson 1981; Peebles 1981a). Press and Vishniac (1980) emphasized that there is no hope for the development of appreciable density fluctuations on scales smaller than Ac-

The problem is relieved if the universe is dominated by massive, weakly interacting particles because density fluctuations on small scales can grow before decoupling. This effect has been widely discussed in the case that the weakly interacting particle mass, mx, is some tens of electron volts (e.g., Doroshkevich et al. 1981 and refer- ences therein). If ß ~ 1, the mass coherence length is broad but perhaps not unacceptable (Peebles 1982 a). The case mx — 1 keV is discussed by Bond, Szalay, and Turner (1982) and Blumenthal, Pagels, and Primack (1982). I discuss here a particularly simple and perhaps important limiting case, mx> \ keV. The main results are the spectrum of mass fluctuations, which seems quite reasonable for the production of galaxies and clusters of galaxies, the statistical character of the background tem- perature fluctuations, and the expected size of the mass density anticorrelation at large separations.

II. CALCULATION I assume zero cosmological constant and ß = 1, the

mass being mainly in weakly interacting particles, mass mx. Following Davis et al. (1981), I take the particle distribution in phase space at u « c in the absence of

LI

© American Astronomical Society • Provided by the NASA Astrophysics Data System

The WMAP satellite (2003) measurements found a2 = 5± 1⇥ 10�6

The CDM Cosmology

From observeational indicateons

Cosmological constant = vacuum energy (dark energy) Modern view: Peebles save speed of the evolution of structure formation

MF-Takahara-Yamashita-Yoshii March 1990 Efstathiou-Sutherland-Maddox 1990Established with CMB : peak at SNIa m-z fainter at high z

N(m)

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w(✓)

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C`

<latexit sha1_base64="C3HNeQis5RmE2MFk9vg810Ct9mM=">AAAB93icbVDLSsNAFL2prxpfVZdugkVwVRJRdFnsxmUF+4A2lMl00g6dTMLMjRBKf8SNCx+49Vfc+TdO2iy09VwuHM65l7lzgkRwja77bZXW1jc2t8rb9s7u3v5B5fCoreNUUdaisYhVNyCaCS5ZCzkK1k0UI1EgWCeYNHK/88iU5rF8wCxhfkRGkoecEjTSGBowgDdgIEzZYA8qVbfmzuGsEq8gVSjQHFS++sOYphGTSAXRuue5CfpTopBTwWZ2P9UsIXRCRqxnqCQR0/50fvfMOTPK0AljZVqiM1d/b0xJpHUWBWYyIjjWy14u/uf1Ugxv/CmXSYpM0sVDYSocjJ08BGfIFaMoMkMIVdzc6tAxUYSiiSoPwVv+8ippX9S8y9rV/WW1flvEUYYTOIVz8OAa6nAHTWgBBYQneIFXK7OerXfrYzFasoqdY/gD6/MHbn2Pwg==</latexit>

` ⇡ 200

<latexit sha1_base64="YOZ22IFYZB0h2j2/RF8/Rqb8sPc=">AAACC3icbVC7TsMwFL0prxJeKYwsFhUSU5VURTBWsDAWiT6ktqoc12mtOnFkO4gq6s7CZ3RlYQAhVn6Ajb/BbTNAy7mydHTOvbq+x485U9p1v63c2vrG5lZ+297Z3ds/cAqHDSUSSWidCC5ky8eKchbRumaa01YsKQ59Tpv+6HrmN++pVExEd3oc026IBxELGMHaSMIpwBQocFNTwBCbkiDgARCUwTVlg91zim7JnQOtEi8jRchQ6zlfnb4gSUgjTThWqu25se6mWGpGOJ3YnUTRGJMRHtC2oREOqeqm81sm6NQofRQIaV6k0Vz9PZHiUKlx6JvOEOuhWvZm4n9eO9HBZTdlUZxoGpHFoiDhSAs0Cwb1maRE87EhmEhm/orIEEtMtIlvFoK3fPIqaZRLXqV0flspVq+yOPJwDCdwBh5cQBVuoAZ1IPAIz/AKb9aT9WK9Wx+L1pyVzRzBH1ifP9shk+0=</latexit>

⇤CDM cosmology as the standard paradigm

<latexit sha1_base64="tPOwbFjWrX/Vza7J0b9RfDrcWi8=">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</latexit>

vs. CDM dominated model

H0 = 67.4 ± 0.5 km/s · Mpc�m = 0.315 ± 0.007�� = 0.686 ± 0.007K = �0 + �� � 1 = 0.0007 ± 0.0019�b = 0.0492 ± 0.0011 (i.e. DM/baryon = 5.4)

<latexit sha1_base64="syAGJCCm9l/mszRMK9SrdxK5gaA=">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</latexit>

from Peebles’ Nobel Lecture 2019

受賞前

受賞後

Cosmology started off with pure thought

To 1965 (= discovery of CMB)

with little pieces of observational indications

1965 to Post CMB

What is CMB

CMB - cosmic structure connexion

Studies of large scale structure

Observational cosmology, or observationally driven, …

Here the great role of Jim Peebles!

END