1. The Cosmic Microwave Background Lecture 2 Elena Pierpaoli

2. Lecture 2 – secondary anisotropies Primary anisotropies: – scattering, polarization and tensor modes – Effect on parameters Secondary anisotropies: gravitational – ISW Early Late Rees-Sciama – lensing Secondary anisotropies: (Re-scattering) – Reionization (uniform and patchy) – Sunyaev-Zeldovich effect (thermal & kinetic)

3. The decomposition of the CMB spectrum Challinor 04

4. Line of sight approach Seljak & Zaldarriaga 06 Synchronous gauge Conformal Newtonian Visibility function g

5. Polarization Due to parity symmetry of the density field, scalar perturbations Have U=0, and hence only produce E modes.

6. Scattering and polarization If there is no U mode to start with, scattering does not generate it. No B mode is generated. Scattering sources polarization through the quadrupole.

7. Tensor modes Parity and rotation symmetry are no longer satisfied with gravity waves. B modes could be generated, along with T and E. In linear perturbation theory, tensor and scalar perturbations evolve independently.

8. The tensor modes expansion Scattering only produces E modes, B Are produced through coupling with E And free streaming.

9. Power spectra for scalar and tensor perturbations Tensor to scalar ratio r=1

10. Effect of parameters Effect of various parameters on the T and P spectrum Effect of various parameters on the T and P spectrum

11. 1)Neutrino mass: Physical effects Fluctuation on scale enters the horizon Neutrinos free-stream Neutrinos do not free-stream (I.e. behave like Cold Dark Matter) Derelativization on fluctuations on expansion Expan. factor a Recombination Radiation dominated Matter dominated heavy  light  (T=0.25 eV) –change the expansion rate –Change matter-radiation equivalence (but not recombination)

12. 2) The relativistic energy density N N  = (  rad     Effects: –change the expansion rate –Change matter-radiation equivalence (but not the radiation temperature, I.e. not recombination) Model for: –neutrino asymmetry –other relativistic particles –Gravitational wave contribution Expan. factor a Recombination Radiation dominated Matter dominated 33 >3 

13. Neutrino species Bell, Pierpaoli, Sigurdson 06

14. Neutrino interactions Bell Pierpaoli Sigurdson 06

15. Late ISW

16. ISW-Galaxy cross correlation Giannantonio 08

17. Rees Sciama effect Seljak 1996

18. Lensing: temperature Lewis & Challinor 2006

19. Lensing: polarization

20. Lensing: B polrization

21. Reionization: overall suppression

22. Reionization: large scale effects t = 0.0845

23. Reionization

24. 4) Neutrinos & reionization Motivation: High redshift reionization required by the TP WMAP CMB power spectrum (t= 0.17), but difficult for stars to reionize “so early”. Decaying particles may provide partial reionization at high redshift. The neutrino decay model  + e Hansen & Heiman 03  e +  e +  H +  H + + e - H + e -  H + + e - + e - Inverse Compton Photoionization Collisional ionization

25. Reionization history mass m = 140-500 MeV, Ee = 0 -180 MeV. time decay:  15 =  10 15  s =   abundance:  -9 Neutrino model parameters Standard parameters   x  Ionization fraction X= n H,ion / n H,total Pierpaoli 2004

26. Power spectra High reionization from decay particles produce a too high optical depth and a too weird TP spectrum High-z reionization from stars still needed Long decay times and low abundances are preferred Pierpaoli 2004 Standard parameters

27. Annihilating matter and reionization Slatyer et al 09 Mapelli Ferrara Pierpaoli 06

28. Ostriker-Vishniac effect & patchy reionization Santos et al 03 Zhang et al 04 OV present even if reionization is uniform

29. The Sunyaev-Zeldovich thermal signature e-e-   cluster Frequencies of observation -Typical dimension: 1-10 arcmin - Typical intensity: 10 -4 K - Signal is independent of cluster ‘s redshift - Signal scales as n e - Need complementary information on redshift from other data. -Both high resolution (SPT, ACT..) And low resolution/all-sky (Planck) planned Cosmology with future surveys: Cluster number counts Cluster power spectrum  T/T = f( ) y y  T e n e

30. Clusters number counts Cluster counts depend mainly on sigma_8, Omega_m, w, and the flux threshold of the survey Aghanim et al 08

31. SZ thermal effect-Power spectrum

32. SZ kinetic effect -Same frequency dependence as CMB (difficult to separate) -typically subdominant to Th SZ (5% of the ThSZ signal)

33. SZ polarization produced by Primordial quadrupole (reducing cosmic variance, probing large scale power) cluster’s transverse velocity Clusters’ magnetic fields Double scattering within the cluster

34. Magnitude of SZ polarization Liu et al 2005