The Cosmic Microwave Background

Lecture 1Elena Pierpaoli

(Cosmic Microwave Background)

Brief History of time

Properties: isotropy and anisotropies

• The CMB radiation is isotropic

• We are moving with respect to the CMB rest frame

• There are tiny anisotropies, imprints of matter-radiation fluctuations.

Space Missions

• PLANCK:• Smaller beam• Lower noise• Polarization • Better frequency coverage

COBE WMAP PlanckYear data received 1992 2003 2009Spatial resolution (deg) 7 0.23 0.08Frequencies (GHz) 30-90 22-94 30–857Polarization no yes yesSensitivity (muK/30' pix) 10.5 (8yrs) 1.4

SDSS sliceMatterRadiation

CMB - Cosmic Microwave Background(Temperature and Polarization)

Observables

Measuring the Fundamental Properties of the Universe

DT(q,f) = S al,m Yl,m (q,f) cl = Sm |al,m|2

d (x) = dr/r (x) d (k) = FT[d (x)] P(k) = < |d (k)|2> Pgal(k) = b2 P(k)

bias

The power spectrum

Nolta et al 08

The decomposition of the CMB spectrum

Challinor 04

Evolution equationsPhotons

Massive neutrinosMassless neutrinos

Cold dark amtter

Baryons

metric

Evolution of fluctuations

Ma & Bertschinger 95

Line of sight approach

Seljak & Zaldarriaga 06

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. 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

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

Nn = (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 (Smith, Pierpaoli, Kamionkowski 2006)

Expan. factor a

Recombination

Radiation dominated Matter dominated3n

>3n

CONSTRAINTS:

Before WMAP: Nn <17

After WMAP:Nn< 6.6

(Pierpaoli MNRAS 2003)

Neutrino species

Bell, Pierpaoli, Sigurdson 06

Neutrino interactions