ModernCOSMOLOGY

Grad Course 2010

Max CamenzindBremen @ 2010

What is Cosmology ?• Cosmology, in strict usage, refers to the

study of the Universe in its totality as it now is (or at least as it can be observed now), and by extension, humanity's place in it. Though the word cosmology is recent, study of the universe has a long history involving science, philosophy, esotericism, and religion. Physical Cosmology is the branch of physics and astrophysics that deals with the study of the physical origins and evolution of the Universe in all ist aspects.

Timetable of the Lecture• W1 - D1: History of Scientific Cosmology• D2: The Observable Universe: Hubble

expansion, CMBR, Large-Scale Structure, Dark Matter, Dark Energy.

• W2: Einstein´s gravity Relativistic Cosmos: Space is Expanding ! Friedman equations, Wavelengths are also stretched. How to observe in an expanding Universe ?

• W3: Modern Cosmological Models (LCDM) and Exotic Essences (Qint-, Brane, DE, Quantum) – Friedmann Universe

• W4: Early Cosmos: Planck Era, Inflation, Quark Soup, Hadronisation, Nucleosyn-thesis and Recombination;

• Standard Model Particle Physics, Supersymmetry; primordial nucleosynthesis

• W5: Inhomogeneous Universe: Growth of structure in Newtonian world; relativistic perturbations in Friedmann;

• Inflation: Why, How, Real ? Slow-roll conditions, quantum fluctuations. Recombination: Relic Photons, Anisotropies.

• W6: Inhomogeneous Universe: Small ripples in density from Early Universe grow linearly to Recombination, Universe on Computer: Simulating the growth of structure Cosmic Web. Everything grows by gravitational attraction to Non-Linear Structure finally to Clusters and Black Holes.

• Galaxy Clusters and Gravitational Lensing: Properties of galaxy clusters, X-ray gas, strong and weak gravitational lenses.

Modern Textbooks• „Cosmology“, by S. Weinberg, Oxford Univ.

Press (2008) **• „The Primordial Density Perturbation“, by D.

Lyth & A. Liddle (Cambridge UP 2009) ****. • „Cosmological Physics“, by John Peacock (CUP

1998) • „Principles of Physical Cosmology“, by P. J. E.

Peebles (Princeton Univ. Press, Princeton, 1993) . • „The Early Universe“ by Kolb and Turner

(Addison-Wesley, New York, 1990) . • „Cosmology and Particle Astrophysics“ by L.

Bergström & A. Goobar (Springer-Verlag 2003).• „Modern Cosmology“, S. Dodelson (Academic

Press 2003) - light version ***

Lecture Notes and Homework• My Homepage:

www.lsw.uni-heidelberg.de/users/mcamenzi M. Camenzind, Lecture Notes on Cosmology (pdf for each Part: I, II, III, …).

• Homepage: Ned Wright: Cosmological Tutorial and FAQ.

• Review articles: http://nedwww.ipac.caltech.edu/level5/basics.html

• Exercises: Every 2nd week, Thursday 8 am.

What is Cosmology ?• Cosmology is the study of the Universe and of its

components (galaxies, DM, photons): • how it formed, • how it has evolved to ist present structure• what is its future. • Modern cosmology grew from ideas before

recorded history. Ancient man asked questions such as "What's going on around me?" which then developed into "How does the Universe work?", the key question that cosmology still is asking.

• To religious studies, cosmology is about a theistically created world ruled by supernatural forces. To scientists, cosmology is about a world of controlled observations elucidated by natural forces – primarily understood today.

• Modern cosmology is on the borderland between science and philosophy, close to philosophy because it asks fundamental questions about the Universe, close to science since it looks for answers in the form of empirical understanding by observation and rational explanation. Thus, theories about cosmology operate with a tension between a philosophical urge for simplicity and a wish to include all the Universe's features versus the total complexity of it all.

Magic cosmology – The Universe of Animals and PlantsLascaux 15000 BC: the Pleiades signal the beginning of Winter time

Neolithic Astronomy in Europe• Neolithic Europe refers to a prehistoric period in

which Neolithic technology was present in Europe, roughly between 7000 BC (the approximate time of the first farming societies) and ~ 2000 BC (marks beginning of the Bronze Age).

West – East directions marked in thombs.• Solar Observatory (circular ditch): Goseck (~ 4000)• Megalithic stone settings in Europe: Stonehenge (2500 – 1600 BC): marks Sun

rising for summer and winter solstices. Seasons were important for farming.

Solar Observatory in Goseck

The yellow lines represent the direction the Sun rises and sets at the winter solstice, while the vertical line shows the astronomical meridian.

Stonehenge

Periodicity in Solar Motion

2500 – 2000 BC

Himmelsscheibe Nebra ~ 2000 BC Hier ein Bild aus der Wikipedia, viel über Fundgeschichte,Alter und Interpretation:

Material: Bronze und Gold

Herstellungszeit ca. 2100 bis 1700 v. Chr.

Vergraben ca. 1600 v. Chr.

Gefunden bei Raubgrabung 19999.10.2008:Münze und Briefmarke

Worldviewchanges

with Time• Each culture

develops imaginations about „the“ Universe.

• Example: „Mechanical“ Universe of

the 18th cent

Modern View of the Universe

Epochs of Scientific Cosmology

• The Aristotelian Universe: Ptolemaios, …• Early Scientific Cosmology: Copernicus, …• The Mechanical Universe: Newton, …• The Great Debate – Islands: Shapley/Curtis • The Expanding Universe: Einstein, de

Sitter, Friedman, Lemaitre, Hubble• Big Bang or Steady State ? Hoyle, …• The Inflationary Universe: Guth, Linde, …• The Quantum Universe: Bojowald, …

The Aristotelian Universe

• Aristotelian cosmology envisioned spheres carrying the planets around the Earth - solid crystalline spheres, according to some, which provided the physical structure of the universe. Late in the 16th century, Tycho Brahe observed comets moving through the solar system. This fact finally shattered the crystalline spheres.

http://www.aip.org/history/cosmology/ideas/journey.htm

…“the natural motion of the Earth ….is towards the center of the universe; that is the reason it is now lying at the center.”

Aristotle, On the Heavens

Geocentric Universe Claudius Ptolemäus, 100-170 AD

Sphere offixed starsis still inuse today forlocalisationof objects

Aristoteles (384-322 BC) believed in the power of spheres (crystalline)

FirstCosmologicalModel –55 crystallinespheres(Aristotle)

Only starsand planets were knownat that time -The Universewas a Universe offixed stars,but the Earthwas middle point

Measuring angles has an old tradition in Europe.

Early Scientific Cosmology• In 1543 Nicholas Copernicus proposed to

switch the places of the Earth and the Sun. He put the Sun in the center of the universe and placed the Earth in revolution around the Sun. To account for the daily motion of the heavens, he set the Earth rotating about its own axis.

• To calculate the positions of planets, Copernicus used elaborate geometrical schemes, much like his Greek and Islamic predecessors.

World of the Solar System

Distance to Pluto: ~ 40 AU(~ 320 light minutes)

Galilei Telescope 1609 400 Years of Astronomy

Kepler Telescope 1611 Refractors

The First Telescopes / 1609-1611

• Das Jahr 2009 ist das Internationale Jahr der Astronomie. Anlass ist das 400-jährige Jubiläum von zwei Ereignissen, die die moderne Astronomie begründet haben:

Im Jahr 1609 nutzte Galileo Galilei zum ersten Mal ein Fernrohr zur Himmelsbetrachtung Jupiter-Monde

• Im selben Jahr veröffentlichte Johannes Kepler sein Buch "Astronomia Nova", in dem er grundlegende Gesetze der Planetenbewegung aufzeigte (die sog. 3 Kepler-Gesetze).

2009 sind viele Aktivitäten geplant.

The firstReflectorTelescopeNewton 1672

D = 33 mmf = 15 cm

400 Years of Telescopesfrom Refractors to VLT

Philosophy and Science -2000 years in retrospect

• Natural sciences always had a great influence on philosophy and on the way we see the world. Until the age of the Renaissance there was no clear distinction between philosophy and science. Physics and astronomy were among the favorite topics of the natural philosophers of the antiquity until the time of Copernicus. The desire to explore the starry heavens and to reveal its secrets is probably as old as mankind itself. However, notable advances in this discipline were made only fairly recently, after the invention of the telescope in the 17th century.

Keplers Laws• Aristotelian physics no longer worked in the

universe of Copernicus and Kepler. A new explanation of how the planets continued to retrace the same paths forever around the Sun remained a central problem of cosmology until Isaac Newton explained how objects move under gravity. He accomplished this by showing how motions in the heavens obey the same laws that determine the movement of bodies on Earth. This led the way to understanding what was increasingly seen as a mechanical universe.

The Mechanical Universe

• Newton treated the motions of the stars and planets as problems in mechanics, governed by the same laws that govern motions on earth. He described the force of gravity mathematically.

• The solar system contains many bodies, and the calculation of the orbit of any planet or satellite is not simply a matter of its gravitational attraction to the body around which it orbits. In addition, other bodies have smaller, but not negligible, effects (called "perturbations"). For example, the Sun alters the Moon's motion around the Earth, and Jupiter and Saturn modify the motions of each other about the Sun.

Newton and the 3 Laws of Motion• Aristotle and Ptolemy laid the foundation for the scientific

understanding of the universe, which remained authoritative for one-and-a-half thousand years. Until the time of Galileo, the Greeks were undisputed in natural science and astronomy.

• Galileo, Copernicus, and Newton changed this. Isaac Newton (1642-1727) revolutionized physics with his proposition that all bodies are governed by the three laws of motion. The first law of motion states that a body continues in a state of rest or continues to be moving uniformly in a straight line unless a force is applied to the object. The second law states that the force applied to an object is proportional to its mass multiplied by acceleration (F=ma). The third law states that for every action there is an equal opposite reaction.

Laplace and the Mechanistic View• Given these natural laws, mankind derived a picture of the

universe that accounts neatly for mass, position, and the motion of the celestial bodies while it interprets the latter as dynamic elements of a celestial apparatus, not unlike that of a mechanical apparatus. It is therefore called the mechanistic worldview. It was elaborated in its purest form by Marquis de Laplace (1749-1827) in his writing Mécanique Céleste.

• The mechanistic view sees the universe as an arrangement in which stars and planets interact with each other like springs and cogs in a clockwork, while God is watching from above. If the initial position and state of all objects in a mechanically determined universe is known, all events can be predicted until the end of time, simply by applying the laws of mechanics. It was further thought that this kind of knowledge is available only to an omniscient God.

• The mechanistic view does not make any statements about the creation of the universe.

Discovery of Speed of Light• In 1676, the Danish astronomer Ole Roemer (1644-1710)

announced a remarkable discovery. He observed seasonal variations in the disappearances of Jupiter's moons behind Jupiter. Because the distance between Earth and Jupiter varies with the seasons, while the Earth travels on its path around the Sun, this means that the light from Jupiter's moons travels either shorter or longer distances throughout the year. The changes in Roemer's observation corresponded with the distances between Earth and Jupiter, which implied that the speed of light is finite. Roemer's observation did, however, not directly contradict the mechanistic worldview.

• In the mechanistic view, light waves travel through the ether, just as sound waves travel through air. - Yet, there was a problem with the concept of "ether". Its existence could never be detected.

Crisis at End of 19th Century• At the end of the 19th century, the mechanistic view was

in trouble. Astronomers noticed that Mercury's perihelion (the closest point to the Sun in its orbit) changed slightly with every orbit. This observation shattered the notion of immutable orbits. Astronomers tried to solve this problem by predicting a mystery planet they called Vulcan, which would account for the observed gravitational variations.

• Michelson and Morley brought the mechanistic worldview into even more trouble. In an experiment, which was designed to measure the velocity of the earth, they found that the speed of light is constant, contrary to what they had expected. They found this characteristic of light to be in disagreement with the Galilean velocity addition formula v´ = v1 + v2, which means their observation contradicted classical mechanics.

The Great Debate – Islands?• At the beginning of the 20th century,

astronomers were unsure of the size of our galaxy. Generally, they believed it was not much greater than a few tens of thousands of light years across, and perhaps considerably less. Also, observations early in the 20th century made it seem that our solar system was near the center of the galaxy.

• This vision of the universe was soon replaced with a revolutionary new conception, based largely on the observations of the American astronomer Harlow Shapley at the Mount Wilson Observatory.

Edwin Hubble and James Jeans at the 100-inch telescope on Mt. Wilson.

1916 – Shapley Distances to GC

• M22, a globular cluster of many thousands of stars. By assuming that certain types of stars here were as bright as similar nearby stars whose distances had been measured, Shapley could estimate the distance to this far object.

The Great Debate – Size of Galaxy• Shapley defended his conclusions in the so-

called "Great Debate" before the National Academy of Sciences on 26 April 1920. His major concern was the size of the galaxy. His model of a drastically larger galaxy, with the solar system far from its center, was largely correct. But he was on less solid ground when he argued that the spiral nebulae, which seemed to be much smaller, were part of our galaxy. His opponent, Heber Curtis, argued that the galaxy could be as large as Shapley said, yet still be only one of many island universes. Ultimately observations would prove Curtis correct, but in 1920 Shapley had the stronger position.

• The centuries-old debate was resolved only by new scientific evidence, produced using larger telescopes and new observational techniques, including photography and spectroscopy. The key proponent of island universes was Edwin Hubble, who like Shapley did his revolutionary work at the Mount Wilson Observatory.

• Early in 1924 Hubble wrote to Shapley again. This time Hubble reported, "You will be interested to hear that I have found a Cepheid variable [star] in the Andromeda Nebula (M31). I have followed the nebula this season as closely as the weather permitted and in the last five months have netted nine novae and two variables."

The Great Debate – Islands ?

The curve of luminosity of the first Cepheid variable star discovered by Edwin Hubble in the Andromeda Nebula, M31. Using this he could determine the nebula's distance [Letter to Shapley in 1924].

Cepheids are Bright Pulsators

1924: Andromeda is a Galaxy

like the Milky Way~ 100 Billion Stars

The Universe in 1928• Before the 1920s ended, astronomers understood

that the spiral nebulae lie outside our own Galaxy. In the previous decade Shapley had multiplied the size of the universe by about ten times. Hubble multiplied it by another ten - if not more. Hubble's universe was no longer the one all-comprehending galaxy envisioned by Shapley. Henceforth the universe was understood to be composed of innumerable galaxies spread out in space, farther than the largest telescope could see. Hubble next would show that the universe is not static, as nearly everyone then believed, but is expanding. What he had made infinite in space, he would make finite in time.

The Expanding Universe• In the early 20th century the common worldview

held that the universe is static. Einstein expressed the general opinion in 1917 after de Sitter produced equations that could describe a universe that was expanding, a universe with a beginning. Einstein wrote him that "This circumstance irritates me." In another letter, Einstein added: "To admit such possibilities seems senseless."

• In 1928 Edwin Hubble attended a meeting of the International Astronomical Union, held that year in Holland. There Hubble discussed cosmological theories with de Sitter. Hubble returned to the Mount Wilson Observatory determined to test de Sitter's theory.

Einstein, de Sitter 1932

Friedman 1922

Einstein Changed Our View• "Falling objects don't feel gravity." Einstein

imagined what it would be like to ride through space on a beam of light and came to the conclusion that space and time can be visualized as coordinate systems, or "reference frames", relative to the observer. This was the basis for his Relativity Theory. At about the same time, other physicists pondered on equally fundamental problems, which concerned interactions of matter and radiation, but came to totally different conclusions than Einstein.

Relativistic Cosmos: Friedman Universe FRW with Friedman-Equations (1922).

Cosmological Constant Problem Cosmological Constant Problem

GGνν+ + ggνν=8=8ππTTνν ++VVggνν

Geometry Geometry

Quantum VacuumQuantum Vacuum

1929: The Hubble-Law

• Relation between Redshift z and Distance D (Hubble 1929):

– v = c z , c: Light velocity– z : relative change in wavelength – H0 : Hubble constant – D is the Distance, D = (c/H0) z– Only valid for small redshifts z < 0,1 ! ( otherwise relativistic corrections)

DHv 0 ×=

Redshift cz ~ Distance

W. Keel 2007

Extension to larger Distances

CosmologicalSN Ia

(Tonry et al. 2003)

Hubble-Law is

violated for z > 0.1

Hub

ble-

Law

Extension to Cosmic Distances

Friedman´s Expanding Universe• In fact a few astronomers had been looking for

other solutions to Einstein's equations. Back in 1922, the Russian meteorologist andmathematician Alexander Friedmann had published a set of possible mathematical solutions that gave a non-static universe. Einstein noted that this model was indeed a mathematically possible solution to the field equations.

• But through the 1920s, neither Einstein nor anyone else took any interest in Friedmann's work, which seemed merely an abstract theoretical curiosity. Most astronomers continued to take it for granted that the real universe was static.

SpaceTime View of theExpansion of the

Universe

3-space isexpanding.Wavelengths also are stretched.

• The expansion of the universe is now seen as one of the great scientific discoveries, and Hubble generally gets the credit. More precisely, however, Hubble established an empirical formula that led the great majority of scentists to believe in the expansion. It is an open historical and philosophical question in what sense Hubble's correlation of data was a "discovery," and exactly how the claim that the universe is expanding grew in scientists' minds.

• Many observations have confirmed the model of an expanding universe that Hubble's relationship validated. But Hubble should not be judged simply by which of his conclusions are now believed to be correct. More important was the direction he pointed out: using galaxies as a key to cosmic history.

1948: Big Bang or Steady State ?

• In 1946 the Ukrainian-born American physicist George Gamow considered how the early stage of an expanding universe would be a superhot soup of particles, and began to calculate what amounts of various chemical elements might be created under these conditions. Gamow was joined by Ralph Alpher, a graduate student at George Washington University, and by Robert Herman, an employee at the Johns Hopkins Applied Physics Laboratory, where Gamow consulted.

• The steady-state Universe proposed by Hoyle, Bondi and Gold (1948) had a major advantage over the Big-Bang expanding universe. In their universe the overall density was kept always the same by the continuous creation of matter. Much later it turned out to be erreneous assumpt.

Steady-Staters: Gold, Bondi & Hoyle

• The idea of a „steady state Universe“ was an erreneous track in the evolution of Cosmology

The Cosmic Microwave• A powerful blow against steady state theory was struck

in 1965 with a surprising discovery. In a 1948 paper, Gamow had argued that the big-bang Universe would at first be dominated by radiation — a raging sea of energy. As this expanded the energy would mostly be converted to matter. Alpher and Herman predicted that a remnant of the radiation would remain - a cosmic background radiation permeating all space. As the Universe expanded, this would cool. Radiation that had initially been far more than white-hot would by now have very low energy. They predicted the temperature of the Universe now should be around 5 degrees Kelvin.

Penzias & Wilson discovered CMB in 1964Earned the Nobelprize in 1978

CMB Spectrum : Blackbody with T0 = 2.725 K

CMB Temperature 2.725 K

Planck mission

CMB - Consequences• The cosmic microwave background radiation

(CMB), discovered in 1964, is a telltale remnant of the early universe. Its very existence is compelling evidence that the universe has evolved from an extraordinarily hot, compact beginning. To have produced radiation with the characteristics of the CMBR, the universe must at one time have been entirely different from what astronomers see today. No galaxies, stars, or planets existed: the universe was filled with elementary particles and radiation at extremely high energies.

COBE/DMR, 1989 - 1992

Gravity is STRONGER in cold spots: ∆T/T ~ Φ/c²

CMBR TemperatureFluctuations(long tradition before COBE 1989)

- Dipole

- Milky Way

Large-scale

∆T/T ~ 10-5

should exist due to clumpiness in the present Universe

Nobel-prize in Physics2006

• John C. Mather (1946)NASA Goddard Space Flight Center, Greenbelt, MD, USA(PhD from Berkeley)

• George F. Smoot (1945)University of California, Berkeley, CA, USA(PhD from MIT)

WilkinsonMicrowaveAnisotropyProbe –WMAP2001-2010

WMAP Dipole

WMAPTemperatureFluctuationson scales > 13‘ multipoles < 800

CMB – Temperature Anisotropies

Resonanceat ~ 0.6 degangular separation

∆T ~ 80 µK

Next: Planck• The third medium-

sized (M3) mission of the Horizon 2000 programme, Planck will measure temperature fluctuations in the CMB with a precision of ~ 2 parts in a million and an angular resolution ~ 5-8 arcmin.

• Launch: 2009 (ESA).

Planck ready for Launch in May 2009

The Universe of Dark Matter

• In astronomy and cosmology, Dark Matter (DM for short)) is hypothetical matter that is undetectable by its emitted radiation, but whose presence can be inferred from gravitational effects on visible matter.

• Dark matter is believed to play a central role in structure formation and galaxy evolution, and has measurable effects on the anisotropy of the cosmic microwave background.

Coma Cluster

The Radial Equilibrium of Disks

For the gas in a disk galaxies, the radial potential gradient provides the acceleration for

the circular motion.

€

2VR

= - ∂ Φ∂ R

≈ GM(R)

2R

where M(R) is the mass enclosed within radius R.

The shape of V(R) can be anything from solid body toV ≈ constant (flat). For larger spirals like our Galaxy,V(R) is usually flat, so ...... ???

• Strong gravitational lensing as observed by the Hubble Space Telescope in Abell 1689 indicates the presence of dark matter.

• By measuring the distortion geometry, the mass of the cluster causing the phenomena can be obtained.

Weak GravLensing

The Inflationary Universe

• In 1979 a young American particle physicist, Alan Guth, proposed that important cosmological features can be explained as natural and inevitable consequences of new theories of particle physics. Guth showed how a huge “inflation” could have taken place in the first minuscule fraction of a second of the universe’s evolution. In this tiny interval the universe could have expanded at an astonishing rate, then slowed down. After only a few years, “inflationary universe” theory merges with the standard Big-Bang theory.

InflationInflation = a brief period of highly accelerated (exponential) expansion, early in the history of the Universe.

Size (meters)

Time (seconds)

Guth´s Inflation

New Inflation

Chaotic Inflation …

There is noUniverse without

Inflation

How Big is the Observable Universe ?Relative to the local curvature & topological scales

Fluctuation Generator

Fluctuation Amplifier

Hot Dense SmoothCool Rarefied

Clumpy

H(z)

(Graphics from Gary Hinshaw/WMAP team)

400

381

At the End of Lecture – know all Params

The Universe of Dark Energy• In 1998, published observations of Type Ia

supernovae by the High-z Supernova Search Team followed in 1999 by the Supernova Cosmology Project suggested that the expansion of the Universe is accelerating.

• In astronomy, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the Universe. Dark energy is the most popular way to explain that the Universe appears to be expanding at an accelerating rate. In the standard model of cosmology, dark energy currently accounts for 74% of the total mass-energy of the Universe.

SNe Ia similar throughout the Universe Nearby SNe Ia

Distant SNe Ia

R(t)

t

scal

e fa

ctor

timeBig BangBig Bang Big CrunchBig Crunchnownow

Dark Energy Causes the Universe to Accelerate Forever!Dark Energy Causes the Universe to Accelerate Forever!

(1) the Universe first slows down (decelerates) because of gravity

(2) the Universe then speeds up forever (accelerates) because of Dark Energy

The Quantum

Universe …

Spiegel 2009Martin Bojowald

… or the Stringy Universe ?

• Since the 1970s, physicists have worked on a “string theory” that they hope can explain all the laws of physics and all the forces of nature in a single equation. In this theory, the basic constituents of the universe are tiny wriggling strings rather than particles. Cosmologists, however, have found no experimental evidence for string theory, nor have they thought up any prediction of observations that could refute it. If some of the original submicroscopic strings were stretched as large as galaxies during the brief inflationary spurt of the early universe, they might now be snapping under enormous tension, and the resulting ripples in space-time might be detectable.

… or extra Dimensions ?

Summary

• Our knowledge about the structure of the Universe evolved slowly over the last 2000 years.

• Since the invention of telescopes in 1609, the imagination evolved from the solar system to the Galaxy and then to the entire world of galaxies.

• The modern view on the Universe is essentially based on the microwave background which signals the beginning of time-evolution and the formation of tiny structures which grow towards the large-scale structure of the present Universe.

• Modern Cosmology struggles with Dark Matter, Dark Energy and the very Origin of the Big-Bang.

Michael Turner @ 2007