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WMAP and Inflation

V. Barger, Hye-Sung Lee, Danny Marfatia

Abstract

We assay how inflationary models whose properties are dominated by the dynamics of a single scalar field are constrained by cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP). We classify inflationary models in a plane defined by the horizon-flow parameters. Our approach differs from that of the WMAP collaboration in that we analyze only WMAP data and take the spectral shapes from slow-roll inflation rather than power-law parameterizations of the spectra. The only other information we use is the measurement of $h$ from the Hubble Space Telescope (HST) Key Project. We find that the spectral index of primordial density perturbations lies in the 1σrange 0.94<n_s<1.04 with no evidence of running. The ratio of the amplitudes of tensor and scalar perturbations is smaller than 0.61 and the inflationary scale is below 2.8\times 10^{16} GeV, both at the 2σC.L. No class of inflation or ekpyrotic/cyclic models is excluded. The λφ^4 potential is excluded at 3σonly if the number of e-folds is assumed to be less than 45.

WMAP and Inflation

Abstract

We assay how inflationary models whose properties are dominated by the dynamics of a single scalar field are constrained by cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP). We classify inflationary models in a plane defined by the horizon-flow parameters. Our approach differs from that of the WMAP collaboration in that we analyze only WMAP data and take the spectral shapes from slow-roll inflation rather than power-law parameterizations of the spectra. The only other information we use is the measurement of from the Hubble Space Telescope (HST) Key Project. We find that the spectral index of primordial density perturbations lies in the 1σrange 0.94<n_s<1.04 with no evidence of running. The ratio of the amplitudes of tensor and scalar perturbations is smaller than 0.61 and the inflationary scale is below 2.8\times 10^{16} GeV, both at the 2σC.L. No class of inflation or ekpyrotic/cyclic models is excluded. The λφ^4 potential is excluded at 3σonly if the number of e-folds is assumed to be less than 45.

Paper Structure

This paper contains 28 equations, 3 figures, 1 table.

Figures (3)

  • Figure 1: Relative likelihood plots for several cosmological parameters and $A_s$. $t_0$ is the age of the Universe in Gyr. We do not show the plot for $h$ because it is not constrained by the fit; see Table. \ref{['tab:limits']}.
  • Figure 2: Relative likelihood plots for some inflationary parameters.
  • Figure 3: 1$\sigma$, 2$\sigma$ and 3$\sigma$ allowed regions in the $\epsilon_2-\epsilon_1$ and $R-n_s$ planes. We have plotted the predictions for the $\lambda \phi^4$ potential with the number of e-folds $N=40$, 50, 60 and 70. The prediction approaches $\epsilon_1=\epsilon_2=0$ ($n_s=1$, $R=0$) as $N\rightarrow \infty$.