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.

Fundamentals of cosmology: Expansion of the Universe

H0 = 72 8 km/s/Mpc(HST key project, 2001)

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

É T=T(nê) É T=T(nê) =P

`a`mY?`m(nê)

C` = hja2`mji

∆T/T ~ 10-5

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

“The Seven Pillars” of the CMB(of inflationary adiabatic fluctuations)

•Large Scale Anisotropies

•Acoustic Peaks/Dips

•Damping Tail

•Polarization

• Gaussianity

•Secondary Anisotropies

•Gravity Waves

Minimal Inflationary parameter set

Quintessesnce

Tensor fluc.

Broken Scale Invariance