cosmology from cmb dmitry pogosyan university of alberta lake louise, february, 2003 lecture 1: what...
TRANSCRIPT
Cosmology from CMB
Dmitry Pogosyan
University of Alberta
Lake Louise, February, 2003
•Lecture 1: What can Cosmic Microwave Background tell us about the Universe ? A theoretical introduction.
•Lecture 2: Recent successes in the mapping of CMB anisotropy: what pre-WMAP and WMAP data reveals.
Matter constituents according to modern view
• P ≈ -ρ ρ = const
• P = 0 ρ = 1/a3
• P ≈ 0 ρ = 1/a3
• P = ρ/3 ρ = 1/a4
• Dark energy ~ 70%• Dark matter ~ 30%• Baryons ~ 5%• 3K Radiation ~0.01%
H2 ñ (a0=a)2 = (8ùG=3)P
úi à K =a2
Òi = úi=(3H2=8ùG) ! i = úi=(3á1002=8ùG)
¿Dark? MatterFundamentals of cosmology:
existence of Large-Scale Structures
8 ~ 1, averaged in spheres of 8 Mpc radius
What do cosmologists want to learn about the Universe ?
• Matter content
• Geometry of the space
• Origin of structures and details of their formation
• Origin of the Universe as we observe now. What theory describes the early epoch of evolution ?
Cosmic Microwave Background
•Discovered 1965 (Penzias & Wilson)
•2.7 K mm-cm wavelentgh
•400 photons/cm3
•Isotropic
•1992 COBE satellite measures anisotropies ~ 10-5
R ? z = 0
Primary Anisotropies
•Tightly coupled Photon-Baryon fluid oscillations
•Linear regime of perturbations
•Gravitational redshifting
Dec
oupl
ing
LSS
Secondary Anisotropies
•Non-Linear Evolution
•Weak Lensing
•Thermal and Kinetic SZ effect
•Etc.
z? ø 1100
~10h-1Mpc
reionization
redshift z
time t14Gyrs 10Gyrs today
Matter constituents at T~3000K• Radiation ~ 20% (r)
• Baryons ~ 15% (b)
• Dark matter ~ 65% (cdm)
• Dark energy ~ 0.000%• Curvature ~ 0.0 ?
Generation of the observable CMB temperature anisotropy at last-scattering
surface• Constitutents: baryons+radiation interacting via
Thompson scattering + dark matter.• Modes: adiabatic/isocurvature, tensor, growing/decaying• Scale: sound horizon rs
• Coherent standing waves • Correlated Effects:
– photon energy perturbation + grav.potential– Doppler effect from moving electrons
• Coherence – one mode, one random, adds in quadrature.
• Effect of massive baryons
K rs
ΔT/T(k)
2 4 5
Formation of CMB anisotropy at last scattering
Adiabatic cosine behaviour
¼ r + ~ Ak cos(k rs)k → 0, dT/T ≠ 0
2
CMB anisotropy at last scattering
2 2
Amplification of short waves when radiation dominatedgravity¼ r + ~ f(k) cos(k rs)
k rs
ΔT/T(k)
2 4 5
Damping of short waves at last scattering
photon diffusion, shear viscosity of plasma, non-instant recombination¼ r + ~ f(k) cos(k rs) exp(-k2/kD
2)
k rs
ΔT/T(k)
2 4 5
Doppler effect (movement of scattering electrons)
Doppler part of dT/T ~ i Ak sin (k rs)
k rs
ΔT/T(k)
2 4 5
Effect of baryon mass
Offset of ¼ r + - constDecrease of electron velocityi Ak sin (k rs) / sqrt(1+3/4 ρb/ρr)
k rs
ΔT/T(k)
Sachs-Wolfe
Acoustic Oscillations
Drag,Doppler
Dampingø 3
1Ð
! b
ø eàk2=k2D
Phenomenology of the Angular Power Spectrum
Tensors T=S ù 7(1à ns)
`pk ø R ?rs(ñ?)
large <-- scales --> small
Mapping the anisotropy patternonto the sky
• Geometry (curvature) of the space• Expansion rate, including presence and
dynamical properties of the vacuum energy (quintessence field ?)
• But, both mainly affect angular diameter distance, thus degeneracy: R/rs = l
• Extra physics, modifying Cl:– ISW (photon propagation through varying grav.pot
(large scales) – Secondary reonization (at z>5) – damping of small
scales. Relates physics of CMB to first stars formation
Less well understood, thus more interesting ingredients, relating CMB to
fundamental physics• Initial conditions – adiabatic -> inflation – slope,
amplitude, potential. Easy to check given theory, less satisfying general case. Until recently, only simplest power-law parameterization was justified by the data quality. With WMAP, situation starts changing.
• Generation of gravitational waves generation is a natural outcome of the early Universe. GW contributes to low l, its contribution is model dependent but to measure it would be an ultimate prize – GR support, mapping inflaton potential directly.
Minimal Set of 7 Cosmological Parameters
b, cdm k, ns,
8c Complex
plasma
at decoupling
b/=0.8
m/=3.5
Geometry of
the Universe
wQ
Initial conditions
(inflationary)
nt, At/As,
broken scale invariance
Late-time damping
due to reionization
Joint pre-WMAP CMB measurements:k= -0.05 0.05 b = 0.022 0.002 ns = 0.95 0.04 cdm = 0.12 0.02
Degeneracies
• Angular diameter of the sound horizonc – 8 as predicted from CMBc – nsc – gravitational waves• Degeracies are especially limiting on partial
data, but some are difficult to break overall• One way – combine CMB data with other
experiments, which place limits on different combinations
• Another way – use polarization
Cosmic Parameter Near-degeneracies
Some parameters are measured better than others. Particular degeneracies correlate some parameters
`peak ø kpeakdA ø r s
dAììrec
Certain combinations of parameters give same projected power spectrum e.g. geometrical degeneracy. If you don’t constrain h and leave matter components unchanged the peaks are projected onto the same l values.
dA ( (ÒË;Òk)
CMB Polarization
• Full description of radiation is by polarization matrix, not just intensity – Stockes parameters, I,Q,U,V
• Why would black-body radiation be polarized ? Well it is not in equilibrium, it is frozen with Plankian spectrum, after last Thompson scattering, which is polarizing process.
• Because, there is local quadrupole anisotropy of the flux scattered of electron. Thus, P and dT/T are intimately related, second sources first (there is back-reaction as well).
• There is no circular polarization generated, just linear – Q,U. Level of polarization ~10% for scalar perturbations, factor of 10 less for tensors. Thus need measurements at dT/T 10-6 – 10-8.
• As field – B, E modes (think vectors, but in application to second rank tensor), distinguished by parity.
Why do we learn more from polarization ?
• No new physics (parameters) just new window to last scattering which is cleaner, albeit signal is weaker.
• Clear signature adiabatic mode.• Grav waves are the only source which produces B-
pattern – direct detection of this fundamental physical effect is possible.
• Breaking degeneracy between parameters, in particular
independent measurement of c