Physical Cosmology 6/6/2016

Physical Cosmology 6/6/2016

Alessandro Melchiorri

alessandro.melchiorri@roma1.infn.it slides can be found here:

oberon.roma1.infn.it/alessandro/cosmo2016

CMB anisotropies

The temperature fluctuation in a direction can be expressed as a line-of-sight integral:

We have 3 terms:

Gravity: photons coming out from CDM potential wells will suffer a redshift.

Intrinsic: where we have more baryons we have more photons (tight coupling) and a blue shift.

Doppler: baryons move and they leave a doppler effect when scattering off photons.

Hu, Sugiyama, Silk, Nature 1997, astro-ph/9604166

Integrated Sachs-Wolfe effect

Late ISW

Early ISW

Late and Early ISW

Late ISW

Early ISW

Late and Early ISW are on different angular scales.

They depend on different parameters.

If you vary Neff you vary EISW.

If you vary w you vary LISW.

Late ISW

Late Integrated Sachs-Wolfe effect

while most cmb anisotropies arise on the last scattering surface, some may be induced by passing through a time varying gravitational potential:

∫ ^Φ ( )

−

= τ τ

δ d

T

T 2

when does the linear potential change?

δ ρ π

2

Φ = 4 G a

∇

• constant during matter domination

• decays after curvature or dark energy come to dominate (z~1) induces an additional, uncorrelated layer of large scale anisotropies

two independent maps

Integrated Sachs-Wolfe map Mostly large angular features

Early time map (z > 4)

Mostly from last scattering surface

Observed map is total of these, and has features of both (3 degree resolution)

compare with large scale structure

potential depth changes as cmb photons pass

through

time dependent

gravitational potential observer

density of galaxies traces the potential depth

ISW fluctuations are correlated with the galaxy distribution!

since the decay happens slowly, we need to see galaxies at high redshifts (z~1)

➢ active galaxies (quasars, radio, or hard x-ray sources)

➢ possibility of accidental correlations means full sky needed

how do we trace the matter?

X-rays from active galaxies

HEAO-1 x-ray satellite

Galaxy and virtually all visible structures cleaned out

Radio galaxies NRAO VLA Sky Survey (NVSS)

Fosalba, Gaztanaga 2004

5 (old) ISW detections

Mean redshift

Signal (µK) Bias Catalog Band

Reference

0.1 0.70 pm 0.32 1.1 2MASS,

infrared

Afshordi et al. 2004

0.15 0.35 pm 0.17 1.0 APM, optical Scranton et al, 2004

0.3 0.26 pm 0.14 1.0 SDSS, optical Fosalba et al.

2004

0.5 0.216 pm 0.1 1.8 SDSS

high z, optical

Padmanabhan et al.

2004

0.9 0.04 pm 0.02 1-2 NVSS+HEAO,

Radio, X-Rays

Boughn &

Crittenden 2004

The gravitational effects of intervening matter bend the path of CMB light on its way from the early universe to the Planck telescope. This “gravitational lensing” distorts our image of the CMB

Gravitational Lensing

A simulated patch of CMB sky – before lensing

10º

Gravitational Lensing

A simulated patch of CMB sky – after lensing

10º

Gravitational Lensing

Planck dark matter distribution throught CMB lensing

This can be obtained using 4-point correlation function

Most significative ISW detection is coming by cross correlating Planck

with CMB lensing

Large angular scales

Small angular scales

Oscillations

are on subdegree angular scales.

They need causality to form !

First peak gives

angular size of horizon at recombination !

(not accurate!)

Anisotropies here just induced

by gravity

Anisotropies here induced by gravity, photon-baryon

pressure and Doppler

CMB polarization

- Unlike temperature anisotropies is generated only by scattering (no SW or ISW).

- Polarization is sourced mainly by the Doppler term.

Peaks in the angular spectrum are out of phase respect to temperature.

- Measuring polarization increases the precision on cosmological parameters.

- On large angular scale polarization can provide constraints on the reionization optical depth.

- CMB polarization provides the best way to detect primordial (created during inflation) gravitational waves.

The reionization optical depth is given by:

At redshift 6<z<20 the intergalactic

hydrogen is “reionized” by UV photons emitted by the first structures.

A proof of this is the lack of Gunn- Peterson effect in Ly-α systems.

We don’t know exactly how and when reionization happened. In the most

common CMB codes is parametrized as:

xe for reion. at

zre=10 f=1

Δ^z=0.1,1.5

Larger z^re means larger τ !

Parameter degeneracy

Some parameter can have very similar effect on the temperature CMB angular spectrum.

For example. the spectral index and the optical depth of reionization are essentially anti correlated.

Polarization can break the degeneracy !

Increasing τ

increases the polarization at large angular scales, i.e. on the scales of the horizon at recombination.

Primordial Perturbations

Inflation produces the spectrum of primordial perturbations that leads to the formation of structures that we observe

today. These perturbations are defined as scalar perturbations.

In general relativity, perturbations can be divided in

scalar (density), vector (vorticity) and tensor (gravitational

waves). Their evolution is independent until perturbations are linear.

Inflation also produces vector and tensor perturbations.

Vector perturbations fade away and are not detectable.

What about tensor perturbations ?

All inflationary models produce gravity waves at some level. If seen they are extremely supporting evidence for inflation !

Temp.

Pol.

Tensor are present only on super

horizon scales at recombination They dissipates

inside the horizon.

Small

polarization is also generated

at the horizon crossing.

Scalar and tensor are independent and the total spectrum is given by the sum of the two in

quadrature.

Unfortunately, for temperature the effect of GW is very similar to increasing the optical depth

or decrasing n^s

The GW contribution is parametrized by the ratio

computed at 0.05 h/Mpc

Gravitational Waves and Polarization

Polarization is however extremely important ! The polarization field

can be decomposed in

curl-free E mode (that are radial around cold spots and tangential over hot spots) and a

divergence-free B mode (vorticity).

Unfortunately also lensing produces B modes.

There is a limit to the value

of r we can

measure from CMB of

about

r=0.0001

Most recent results limits r<0.09 at 95% c.l.

Measuring primordial GW can help in discriminating between models of inflation

Current best fit model (Starobinsky) predicts r≈0.003