The Cosmic Microwave Background Lecture 1 Elena Pierpaoli

Brief History of time (Cosmic Microwave Background)

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

Measuring the Fundamental Properties of the Universe Radiation Observables Matter SDSS slice CMB - Cosmic Microwave Background (Temperature and Polarization) DT(q, f) = S a c = S |a |2 l m l, m Yl, m (q, f) d (x) = dr/r (x) d (k) = FT[d (x)] P(k) = < |d (k)|2> Pgal(k) = b 2 P(k) bias

The power spectrum Nolta et al 08

The decomposition of the CMB spectrum Challinor 04

Evolution equations Photons Cold dark amtter Baryons metric Massive neutrinos Massless neutrinos

Evolution of fluctuations Ma & Bertschinger 95

Line of sight approach 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 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 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 e. V) – change the expansion rate – Change matter-radiation equivalence (but not recombination) Expan. factor a

2) The relativistic energy density N N = (rrad - rg) / r 1 Matter dominated Radiation dominated 3 Expan. factor a >3 Recombination • Effects: CONSTRAINTS: – change the expansion rate – Change matter-radiation equivalence (but not the Before WMAP: N <17 radiation temperature, I. e. not recombination) After WMAP: N < 6. 6 • Model for: – neutrino asymmetry – other relativistic particles – Gravitational wave contribution (Smith, Pierpaoli, Kamionkowski 2006) (Pierpaoli MNRAS 2003)

Neutrino species Bell, Pierpaoli, Sigurdson 06

Neutrino interactions