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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

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

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

Space Missions


  • Smaller beam

  • Lower noise

  • Polarization

  • Better frequency coverage


Measuring the Fundamental Properties of the Universe



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)


The power spectrum

Nolta et al 08

The decomposition of the CMB spectrum

Challinor 04

Evolution equations


Cold dark amtter



Massive neutrinos

Massless neutrinos

Evolution of fluctuations

Ma & Bertschinger 95

Line of sight approach

Seljak & Zaldarriaga 06


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

Fluctuation on scale  enters the horizon


Expan. factor a

Matter dominated

Radiation dominated

Neutrinos free-stream


Neutrinos do not free-stream

(I.e. behave like Cold Dark Matter)



(T=0.25 eV)

1)Neutrino mass: Physical effects

on fluctuations

on expansion

  • change the expansion rate

  • Change matter-radiation equivalence (but not recombination)

Expan. factor a

Matter dominated

Radiation dominated


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)


Before WMAP: N <17

After WMAP:N< 6.6

(Pierpaoli MNRAS 2003)

Neutrino species

Bell, Pierpaoli, Sigurdson 06

Neutrino interactions

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