UNITS, NOTATION

1. COSMOLOGY I & II UNITS, NOTATION Energy = mass = GeV Time = length = 1/GeV c = ħ= kB = 1 Metric signature = (1,-1,-1,-1) Planck mass MP = 1.22  1019 GeV Newton’s constant G = 1/ MP 1 eV = 11000 K 1 s ~ 1/MeV 2

2. 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 ¯

3. (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

4. 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

5. 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)

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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)

12. 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)

13. 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)

14. timeline • Temperature ~<kinetic energy> • Thermal equilibrium, radiation dominated universe: T2t ~ 0.3/g1/2 degrees of freedom

15. String theory? GR: time coordinate begins E=1019 GeV Transition from quantum to classical Period of superluminal expansion (cosmic inflation) Cold universe E=1012 GeV release of the energy driving inflation (reheating) beginning of hot big bang and normal adiabatic Hubble expansion RT=const. thermalization; energy dominated by radiation = UR particles Supersymmetric Standard Model? sphaleron transitions wash away primordial baryon asymmetry T = 1 TeV

16. all Standard Model dofs present in plasma Higgs field condenses T = 200 GeV Electroweak phase transition particles become massive baryogenesis? t-quarks annihilate generation of relic cold dark matter? T = 80 GeV Z,W annihilate T = 5 GeV b-quarks annihilate T = 1.5 GeV c-quarks annihilate free quarks, antiquarks and gluons nq= ne= n= 3n/4 T = 200 MeV QCD phase transition _ _ p,n,p,n,  + unstable baryons baryon-antibaryon annihilation

17. np=nn << n neutrino freeze-out T = 2 MeV kinetic equilibrium by virtue of np↔e+, pe-↔n etc. T = 0.7 MeV p and n fall out of equilibrium free neutron decay begins T = 0.5 MeV photodissociation of 3H e+e- annihilation end of free n decay T = 0.1 MeV synthesis of 4He begins synthesis of light elements almost complete t = 180 s matter-radiation equality Dark energy starts to dominate t = 3.8 × 105 yrs photon-baryon decoupling  CMB structure formation