Transcript The Cosmic Microwave Background Lecture 2 Elena Pierpaoli Lecture 2 – secondary anisotropies • Primary anisotropies: – scattering, polarization and tensor modes – Effect on parameters •

The Cosmic Microwave
Background
Lecture 2
Elena 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
Visibility function g
Conformal Newtonian
Synchronous gauge
Seljak & Zaldarriaga 06
Polarization
Due to parity symmetry of the density field, scalar perturbations
Have 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
In linear perturbation theory, tensor and scalar perturbations evolve independently.
Parity and rotation symmetry are no longer satisfied with gravity waves.
B modes could be generated, along with T and E.
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
on fluctuations
Fluctuation on scale  enters the horizon
Derelativization
Neutrinos free-stream
Neutrinos do not free-stream
(I.e. behave like Cold Dark Matter)
on expansion
heavy
Radiation dominated
Matter dominated
light
Recombination
(T=0.25 eV)
– change the expansion rate
– Change matter-radiation equivalence (but not recombination)
Expan. factor a
2) The relativistic energy density Nn
Nn = (rrad - rg) / r1n
Radiation dominated
3n
Expan. factor a
Matter dominated
>3n
Recombination
• 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
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
Inverse Compton
e+g
e+g
Photoionization
H+g
H+ + e-
Collisional ionization
H + e-
H+ + e- + e-
Neutrino model
parameters
Reionization history
Pierpaoli 2004
• mass mn = 140-500 MeV ,
• Ee = 0 -180 MeV.
• time decay: t15 = t/ 1015 s = 210
• abundance: Wn = 10-9
Ionization fraction
X= nH,ion / nH,total
Standard parameters
Wn x
Power spectra
Standard parameters
Pierpaoli 2004
• 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
Annihilating matter and reionization
Mapelli Ferrara Pierpaoli 06
Slatyer et al 09
Ostriker-Vishniac effect & patchy reionization
Zhang et al 04
Santos et al 03
OV present even if reionization is uniform
The Sunyaev-Zeldovich thermal
signature
cluster
g
Frequencies of observation
DT/T = f(n) y
g
e-
y  Te ne
-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
Cluster number counts
Cosmology with future surveys:
Cluster power spectrum
Clusters number counts
Aghanim et al 08
Cluster counts depend mainly on sigma_8, Omega_m, w, and the flux threshold of the survey
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