The cosmic microwave background
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The Cosmic Microwave Background. Lecture 1 Elena 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

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The Cosmic Microwave Background

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The cosmic microwave background

The Cosmic Microwave Background

Lecture 1

Elena Pierpaoli


The cosmic microwave background

(Cosmic Microwave Background)

Brief History of time


Properties isotropy and anisotropies

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

Space Missions

  • PLANCK:

  • Smaller beam

  • Lower noise

  • Polarization

  • Better frequency coverage


The cosmic microwave background

Observables

Measuring the Fundamental Properties of the Universe

Radiation

Matter

SDSS slice

CMB - Cosmic Microwave Background

(Temperature and Polarization)

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

The power spectrum

Nolta et al 08


The decomposition of the cmb spectrum

The decomposition of the CMB spectrum

Challinor 04


Evolution equations

Evolution equations

Photons

Cold dark amtter

Baryons

metric

Massive neutrinos

Massless neutrinos


Evolution of fluctuations

Evolution of fluctuations

Ma & Bertschinger 95


Line of sight approach

Line of sight approach

Seljak & Zaldarriaga 06


Polarization

Polarization

Due to parity symmetry of the density field, scalar perturbations

Have U=0, and hence only produce E modes.


Scattering and polarization

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

Tensor modes

Parity and rotation symmetry are no longer satisfied.

B modes could be generated, along with T and E.


The tensor modes expansion

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

Power spectra for scalar and tensor perturbations

Tensor to scalar ratio r=1


Effect of parameters

Effect of parameters

  • Effect of various parameters on the T and P spectrum


1 neutrino mass physical effects

Fluctuation on scale  enters the horizon

Derelativization

Expan. factor a

Matter dominated

Radiation dominated

Neutrinos free-stream

heavy

Neutrinos do not free-stream

(I.e. behave like Cold Dark Matter)

light

Recombination

(T=0.25 eV)

1)Neutrino mass: Physical effects

on fluctuations

on expansion

  • change the expansion rate

  • Change matter-radiation equivalence (but not recombination)


2 the relativistic energy density n n

Expan. factor a

Matter dominated

Radiation dominated

Recombination

2) The relativistic energy density Nn

Nn = (rrad - rg) / r1n

3

>3

  • 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)

CONSTRAINTS:

Before WMAP: N <17

After WMAP:N< 6.6

(Pierpaoli MNRAS 2003)


Neutrino species

Neutrino species

Bell, Pierpaoli, Sigurdson 06


Neutrino interactions

Neutrino interactions


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