1. 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.

2. Fundamentals of cosmology: Expansion of the Universe H 0 = 72  8 km/s/Mpc (HST key project, 2001)

3. Matter constituents according to modern view P ≈ -ρ ρ = const P = 0 ρ = 1/a 3 P ≈ 0 ρ = 1/a 3 P = ρ/3 ρ = 1/a 4 Dark energy ~ 70% Dark matter ~ 30% Baryons ~ 5% 3K Radiation ~0.01%

4. ¿Dark? Matter Fundamentals of cosmology: existence of Large-Scale Structures  8 ~ 1, averaged in spheres of 8 Mpc radius

5. 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 ?

6. Cosmic Microwave Background Discovered 1965 (Penzias & Wilson) 2.7 K mm-cm wavelentgh 400 photons/cm 3 Isotropic 1992 COBE satellite measures anisotropies ~ 10 -5

8. Primary Anisotropies Tightly coupled Photon-Baryon fluid oscillations Linear regime of perturbations Gravitational redshifting Decoupling LSS Secondary Anisotropies Non-Linear Evolution Weak Lensing Thermal and Kinetic SZ effect Etc. ~10h -1 Mpc reionization 14Gyrs 10Gyrs today

10. ∆T/T ~ 10 -5

11. Matter constituents at T~3000K Radiation ~ 20% (  r ) Baryons ~ 15% (  b ) Dark matter ~ 65% (  cdm ) Dark energy ~ 0.000% Curvature ~ 0.0 ?

12. 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 r s 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

13. K r s ΔT/T(k)  22 44 55 Formation of CMB anisotropy at last scattering Adiabatic cosine behaviour ¼  r +  ~ A k cos(k r s ) k → 0, dT/T ≠ 0

14.  22 CMB anisotropy at last scattering 22 22 Amplification of short waves when radiation dominated gravity ¼  r +  ~ f(k) cos(k r s ) k r s ΔT/T(k)

15. 22 44 55 Damping of short waves at last scattering photon diffusion, shear viscosity of plasma, non-instant recombination ¼  r +  ~ f(k) cos(k rs) exp(-k 2 /k D 2 ) k r s ΔT/T(k)

16.  22 44 55 Doppler effect (movement of scattering electrons) Doppler part of dT/T ~ i A k sin (k r s ) k r s ΔT/T(k)

17.  22 44 55 Effect of baryon mass Offset of ¼  r +  - const Decrease of electron velocity i A k sin (k r s ) / sqrt(1+3/4 ρ b /ρ r ) k r s ΔT/T(k)

18. Sachs-Wolfe Acoustic Oscillations Drag, Doppler Damping Phenomenology of the Angular Power Spectrum Tensors large small

20. Mapping the anisotropy pattern onto 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

23. 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.

24. Minimal Set of 7 Cosmological Parameters  b,  cdm  k,   n s,  8 cc Complex plasma at decoupling  b /   =0.8  m /   =3.5 Geometry of the Universe w Q Initial conditions (inflationary) n t, A t /A s, broken scale invariance Late-time damping due to reionization Joint pre-WMAP CMB measurements:  k = -0.05  0.05  b = 0.022  0.002 n s = 0.95  0.04  cdm = 0.12  0.02

25. Degeneracies Angular diameter of the sound horizon  c –  8 as predicted from CMB  c – ns  c – 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

26. Cosmic Parameter Near-degeneracies Some parameters are measured better than others. Particular degeneracies correlate some parameters 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.

29. 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.

30. 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

34. “ 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