The WMAP normalization of inflationary cosmologies

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The WMAP normalization of inflationary cosmologies

• David Parkinson
• with Andrew Liddle, Sam Leach and Pia Mukherjee
• astro-ph/0607275

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The CMB

• Is plasma physics the only thing we measure with
  the CMB? No!
• Most (90) of structure formed from Gaussian,
  acausal (superhorizon), adiabatic, near
  scale-invariant, scalar perturbations.
• Anisotropies in the CMB fix the amplitude of
  these perturbations, as well as measuring the
  scale-dependence (tilt, running. etc.)

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Inflation

• Inflation - a period of accelerated expansion in
  the very early universe
• Currently the best explanation for the creation
  of these perturbations (also predict tensors - as
  yet unseen).
• Quantum fluctuation -gt initial condition of
  perturbation

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Gravitational Potentials

• CMB photons climb out of gravitational potential
  wells at recombination (Sachs-Wolfe effect)
• Sets amplitude of temperature power spectrum
• Used to normalize inflation

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Amplitude
The normalization ?H as a function of n and r for
WMAP3, specified at a scale of 0.05 Mpc-1
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Normalization

• Bunn, Liddle and White (1995) used 4-year COBE TT
  data to create fitting formula for n (tilt) and r
  (tensor to scalar ratio)
• We use 3 year WMAP TT, TE and EE data to do the
  same thing
• They are different because they are normalized to
  different scales

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The k-l relation

• There is no unique pivot point independent of r
• For r0, k0.004 Mpc-1, while for r0.75, k0.02
  Mpc-1
• Use spike initial Pk to find k-l relation
• So for r0, l60, while for r0.75, l280

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Inflationary Models

• The energy scale of (single-field slow-roll)
  inflation relates to the amplitude through the
  slow-roll parameter ? (or the tensor-scalar ratio
  r)
• Substituting in the WMAP normalization

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Conclusions

• We have determined the WMAP normalization of the
  density power spectrum as a function of the
  inflationary parameters n and r.
• This is an improvement on the accuracy of the
  COBE normalization by a factor of 2.
• The normalization formula can be used to
  constrain models of inflation.

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