The Cosmic Microwave Background

Lecture 2Elena Pierpaoli

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)

The decomposition of the CMB spectrum

Challinor 04

Line of sight approach

Seljak & Zaldarriaga 06

Synchronous gauge

Conformal Newtonian

Visibility function g

Polarization

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

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.

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.

The tensor modes expansion

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

Power spectra for scalar and tensor perturbations

Tensor to scalar ratio r=1

Effect of parameters

• Effect of various parameters on the T and P spectrum

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 dominatedheavy

light

(T=0.25 eV) – change the expansion rate – Change matter-radiation equivalence (but not recombination)

2) The relativistic energy density Nn

N n = (rrad - rg) / r1n

• 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 dominated3

>3

Neutrino species

Bell, Pierpaoli, Sigurdson 06

Neutrino interactions

Bell Pierpaoli Sigurdson 06

Late ISW

ISW-Galaxy cross correlation

Giannantonio 08

Rees Sciama effect

Seljak 1996

Lensing: temperature

Lewis & Challinor 2006

Lensing: polarization

Lensing: B polrization

Reionization: overall suppression

Reionization: large scale effects

t = 0.0845

Reionization

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

n p + e

Hansen & Heiman 03

e + ge + gH + g H+ + e-

H + e- H+ + e- + e-

Inverse Compton

Photoionization

Collisional ionization

Reionization history

• mass mn = 140-500 MeV ,• Ee = 0 -180 MeV. • time decay: t15 = / t 1015 s =

2-10 • abundance: = 10Wn -9

Neutrino model parameters

Standard parameters

x

Ionization fraction

X= nH,ion / nH,total

Pierpaoli 2004

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 2004Standard parametersx

Annihilating matter and reionization

Slatyer et al 09

Mapelli Ferrara Pierpaoli 06

Ostriker-Vishniac effect & patchy reionization

Santos et al 03

Zhang et al 04

OV present even if reionization is uniform

The Sunyaev-Zeldovich thermal signature

e-

gg

clusterFrequencies of observation

-Typical dimension: 1-10 arcmin- Typical intensity: 10-4 K - Signal is independent of cluster ‘s redshift- Signal scales as ne

- 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

DT/T = f(n) y

y Te ne

Clusters number counts

Cluster counts depend mainly on sigma_8, Omega_m, w, and the flux threshold of the survey

Aghanim et al 08

SZ thermal effect-Power spectrum

SZ kinetic effect

-Same frequency dependence as CMB(difficult to separate)

-typically subdominant to Th SZ(5% of the ThSZ signal)

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

Magnitude of SZ polarization

Liu et al 2005