Cosmology I & II

• Expanding universe• Hot early universe• Nucleosynthesis• Baryogenesis• Cosmic microwave background (CMB)• Structure formation• Dark matter, dark energy• Cosmic inflation

UNITS, NOTATION

c = ħ= kB = 1 Energy = mass = GeV

Time = length = 1/GeV

Planck mass MP = 1.22 1019 GeV

Newton’s constant G = 1/ MP

1 eV = 11000 K

1 s ~ 1/MeV

2

Metric signature = (1,-1,-1,-1)

Quantities, observables

• Hubble rate = expansion rate of the universe = H

• Energy density of particle species x = x= E/V

• Number density nx = N/V• Relative He abundance Y = 4He/(H+4He)• Baryon number of the universe (nB-nB)/n

• Scattering cross section ~ [1/energy2], (decay) rate ~ [energy] ~ n

¯

(cont)

• CMB temperature T() = T0 + T() (”CMB power spectrum”)

• Galaxy-galaxy correlators (”Large scale structure” = LSS)

• Distant supernova luminosities

The starting point

• expansion of the universe is very slow (changes adiabatic): H << scattering rates

• Thermal equilibrium (+ some deviations from: this is where the interesting physics lies)

• Need: statistical physics, particle physics, some general relativity

History of cosmology

• General theory of relativity 1916– First mathematical theory of the universe– Applied by Einstein in 1917– Problem: thought that universe = Milky Way

→ overdense universe → must collapse → to recover static universe must introduce cosmological constant (did not work)

Theory develops …

• Willem de Sitter 1917– Solution to Einstein equations, assuming

empty space: (exponential) expansion (but can be expressed in stationary coordinates)

• Alexander Friedmann 1922– Solution to Einstein eqs with matter: no static

solution– Universe either expanding or collapsing

Observations

• Henrietta Leavitt 1912– Cepheids: luminosity and period related →

standard candles

• Hubble 1920s– 1923: Andromeda nebula is a galaxy (Mount

Wilson 100” telescope sees cepheids)– 1929: redshifts of 24 galaxies with

independent distance estimates → the Hubble law v = Hd

• Georges Lemaitre 1927: ”primeaval atom”– Cold beginning, crumbling supernucleus (like

radioactivity)

• George Gamow: 1946-1948– Hot early universe (nuclear physics ~ the Sun)– Alpher, Gamow, Herman 1948: relic photons

with a temperature today of 5 K– Idea was all but forgotten in the 50’s

Demise of the steady state

• Fred Hoyle 1950s– ”steady state theory”: the universe is infinite

and looks the same everywhere– New matter created out of vacuum →

expansion (added a source term into Einstein eqs.)

• Cambridge 3C galaxy survey 1959– Radiogalaxies do not follow the distribution

predicted by steady state theory

Rediscovery of Big Bang

• Penzias & Wilson 1965 Bell labs– Testing former Echo 6 meter radioantenna to use it

for radioastronomy (1964)– 3 K noise that could not be accounted for– Dicke & Peebles in Princeton heard about the result

→ theoretical explanation: redshifted radiation from the time of matter-radiation decoupling (”recombination”) = CMB

– Thermal equilibrium → black body spectrum– Isotropic, homogenous radiation: however, universe

has structure → CMB must have spatial temperature variations of order 10-5 K

Precision cosmology

• COBE satellite 1992– Launch 1989, results in 1992– Scanned the microwave sky with 2 horns and

compared the temperature differences– Found temp variations with amplitude 10-5 K,

resolution < 7O

• Balloon experiments end of 90’s– Maxima, Boomerang: first acoustic peak discovered

• LSS surveys – 2dF etc 90’s; ongoing: Sloan Digital Sky Survey

(SDSS)

• WMAP 2003– High precision spectrum of temperature

fluctuations– Determination of all essential cosmological

parameters with an accuracy of few %

• Big bang nucleosynthesis 1980’s →– H, He, Li abundances (N, )

• Planck Surveyor Mission 2007 (Finland participates)

Surprises/problems

• Dark matter (easy)

• Dark energy (~ cosmological constant, very hard)

• Cosmic inflation (great, but how?)

• Baryogenesis (how?- Standard Model not enough)