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)

COSMOLOGY I & IICOSMOLOGY I & II

Quantities, observables

• Hubble rate = expansion rate of the universe = H

• Energy density of particle species x: x= Ex/V• Number density nx = Nx/V• Relative energy density x = x/c

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

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

¯

critical

(cont)

• CMB temperature T(x,y) = T0 + T(x,y)

• CMB power spectrum P()~< T(x)T(y) >

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

• Distant SNIa 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 2008 (Finland participates)

Surprises/problems

• Dark matter (easy, maybe next year)

• Dark energy (~ cosmological constant?, very hard)

• Cosmic inflation (great, but how?)

• Baryogenesis (how?- Standard Model not enough)

timeline

• Temperature ~<kinetic energy>

• Thermal equilibrium, radiation dominated universe: T2t ~ 0.3/g1/2

degrees of freedom

Period of superluminal expansion(cosmic inflation)

Cold universe

E=1019 GeV Transition from quantum toclassical

String theory? GR: time coordinate begins

E=1012 GeV

release of the energy driving inflation(reheating)

beginning of hot big bang andnormal adiabatic Hubble expansionRT=const.

thermalization; energy dominatedby radiation = UR particles

T = 1 TeV sphaleron transitions wash awayprimordial baryon asymmetry

SupersymmetricStandard Model?

Electroweak phase transitionHiggs field condenses

particles become massive

free quarks, antiquarks and gluons

T = 200 GeV

T = 5 GeV

T = 200 MeV

baryon-antibaryon annihilation

QCD phase transition

T = 80 GeV Z,W annihilate

p,n,p,n, + unstable baryons _ _

c-quarks annihilateT = 1.5 GeV

b-quarks annihilate

nq= ne= n= 3n/4

all Standard Model dofspresent in plasma

baryogenesis?

generation of relic cold dark matter?t-quarks annihilate

neutrino freeze-out

p and n fall out of equilibriumfree neutron decay begins

photodissociation of 3H

end of free n decay synthesis of 4He begins

synthesis of light elements almostcomplete

np=nn << n

T = 2 MeV

T = 0.7 MeV

T = 0.1 MeV

t = 180 s

t = 3.8 × 105 yrsmatter-radiation equalityDark energy starts to dominatephoton-baryon decoupling CMB

T = 0.5 MeV e+e- annihilation

kinetic equilibrium by virtue ofnp↔e+, pe-↔n etc.

structure formation