The WMAP normalization of inflationary cosmologies

TL;DR

The paper computes the WMAP3 normalization of the matter power spectrum as a function of inflationary parameters $n$ and $r$, keeping the dependence on these parameters explicit rather than marginalizing them away. Using a grid of fixed $n$ and $r$ values in CosmoMC with WMAP data, it derives a compact fitting function for the normalization $\delta_H^{WMAP}(n,r)$ and identifies a pivot scale that depends on $r$. It also links the normalization to the inflationary energy scale via $V_*^{1/4}/M_{Pl} = ((75 \pi^2)/8)^{1/4} r^{1/4} \delta_H^{1/2}$ and reports a 3% statistical uncertainty, with ~0.5% calibration uncertainty. The result improves the precision over the old COBE normalization and provides a practical, model-aware normalization for testing inflationary scenarios against CMB observations.

Abstract

We use the three-year WMAP observations to determine the normalization of the matter power spectrum in inflationary cosmologies. In this context, the quantity of interest is not the normalization marginalized over all parameters, but rather the normalization as a function of the inflationary parameters n and r with marginalization over the remaining cosmological parameters. We compute this normalization and provide an accurate fitting function. The statistical uncertainty in the normalization is 3 percent, roughly half that achieved by COBE. We use the k-l relation for the standard cosmological model to identify the pivot scale for the WMAP normalization. We also quote the inflationary energy scale corresponding to the WMAP normalization.

Figures (2)

• Figure 1: The WMAP3 normalization $\delta_{{\rm H}}$ as a function of $n$ for the four choices of $r$, specified at the scale $0.05 \, {\rm Mpc}^{-1}$. The uncertainties shown are the standard deviations inferred from the Markov chains.
• Figure 2: The relation between multipole $\ell$ and wavenumber $k$ for the best-fit cosmology to WMAP3 data wmap3.