Transcript Document

COSMOLOGY I & II
UNITS, NOTATION
c = ħ= kB = 1
Metric signature = (1,-1,-1,-1)
Energy = mass = GeV
Time = length = 1/GeV
Planck mass MP = 1.22  1019 GeV
Newton’s constant G = 1/ MP2
1 eV = 11000 K
1 s ~ 1/MeV
Quantities, observables
• Hubble rate = expansion rate of the
universe = H
• Energy density of particle species x: x=
Ex/V
• Number density nx = Nx/V
critical
• Relative energy density x = x/c
• Relative He abundance Y = 4He/(H+4¯He)
• Baryon number of the universe (nB-nB)/n
• Scattering cross section  ~ [1/energy2],
(decay) rate  ~ [energy] ~ n
(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
String theory?
GR: time coordinate begins
E=1019 GeV
Cold universe
E=1012 GeV
release of the energy driving inflation
(reheating)
thermalization; energy dominated
by radiation = UR particles
Transition from quantum to
classical
Period of superluminal expansion
(cosmic inflation)
beginning of hot big bang and
normal adiabatic Hubble expansion
RT=const.
Supersymmetric
Standard Model?
T = 1 TeV
sphaleron transitions wash away
primordial baryon asymmetry
all Standard Model dofs
present in plasma
Higgs field condenses
T = 200 GeV
particles become massive
T = 80 GeV
T = 5 GeV
T = 1.5 GeV
Electroweak phase transition
baryogenesis?
t-quarks annihilate
generation of relic cold dark matter?
Z,W annihilate
b-quarks annihilate
c-quarks annihilate
free quarks, antiquarks and gluons
nq= ne= n= 3n/4
T = 200 MeV
__
p,n,p,n,  + unstable baryons
QCD phase transition
baryon-antibaryon annihilation
np=nn << n
T = 2 MeV
kinetic equilibrium by virtue of
np↔e+, pe-↔n etc.
T = 0.7 MeV
neutrino freeze-out
p and n fall out of equilibrium
free neutron decay begins
photodissociation of 3H
T = 0.5 MeV
e+e- annihilation
end of free n decay
T = 0.1 MeV
synthesis of 4He begins
t = 180 s
t = 3.8 × 105 yrs
structure formation
synthesis of light elements almost
complete
matter-radiation equality
Dark energy starts to dominate
photon-baryon decoupling  CMB