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 $h$ from the Hubble Space Telescope (HST) Key Project. We find that the spectral index of primordial density perturbations lies in the 1\sigma range 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 2\sigma C.L. No class of inflation or ekpyrotic/cyclic models is excluded. The \lambda \phi^4 potential is excluded at 3\sigma only if the number of e-folds is assumed to be less than 45.