The cosmic microwave background

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The cosmic microwave background
From cosmology

• to signal processing

CMB (WMAP)
Morlet wavelet
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Overview

• Cosmology
• Basic definition
• State of the art (concordance cosmological model)
• CMB
• Electromagnetic signal on the sky
• Best laboratory for precision cosmology
• Signal processing on the sphere
• Stochastic signal
• Angular power spectrum
• Beyond the concordance model
• Gaussianity and statistical isotropy
• Spherical wavelets

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I. Cosmology

• Cosmology understanding the structure and
  evolution of the universe
• Theory vs. observation concordance cosmological
  model

Cosmological principle homogeneity isotropy
Age T0 13.7 109 yrs Rate H0
71km/s/Mpc Accelerated
Weird energy recipe Ordinary matter ? Ob
0.05 Dark matter ? Odm 0.25 Dark Energy
? O? 0.70
Expansion from Big Bang
Flat geometry
Primordial inflation seeds for LSS
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II. CMB

• 60s electromagnetic microwave radiation
  observed
• Blackbody
• Isotropy around T 3 ?K
• Signature of the cosmological principle
• Identification with CMB
• Primordial plasma matter-radiation
• Radiation decoupling 380.000 years
• after the big bang
• 90s COBE
• T 2.725 0.002 ?K
• BUT predicted anisotropies ?T/T 10-5
• Signature of primordial energy density
  perturbations at inflation
• Signature of structure and evolution of the
  universe

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Precision cosmology

• From COBE to WMAP satellite mission towards
  precision cosmology

COBE 90s
WMAP ongoing
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III. Signal processing on the sphere

• Physics inflation - cosmological
  principle - one universe
• Signal stochastic and gaussian -
  stationary - unique realization
• Analysis (WMAP) two-point correlations
• angular power spectrum Cl
• Best unbiased estimator
• Cosmic variance (non-ergodicity)
• ? Concordance cosmological model

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IV. Beyond the concordance model

• Physics beyond inflation -
  cosmological principle
• Signal non-gaussian - non-stationary
  (statistical anisotropy)
• Space-scale analysis of the maps spherical
  wavelets

Singular features non -gaussianities
Localized analyses
Signal and foreground WMAP map at 94GHz
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Non-gaussianity with wavelets

• Spherical wavelet analysis and non-gaussianity
• Real space maps ? wavelet space (enhanced
  singularities)
• Skewness and excess kurtosis
• Vielva et al. Axisymmetrical spherical mexican
  hat
• Excess kurtosis at 99.8 c.l. one spot at
  scale 10?
• McEwen et al. Real Morlet wavelet (global
  direction)
• Skewness at 99 c.l. one spot at scale 26?
  with given orientation
• Project Steerable wavelets for directional
  analysis
• Match all non-gaussianities
• Identify their local direction
  

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Conclusion
We entered an era of precision cosmology with the
CMB analysis Many questions remain, notably
about the nature of gravitation was Einstein
right?
? astro-ph/0407208 ? astro-ph/0407508 ?
EPFL-ITS-00.2004