Natural inflation: Status after WMAP 3-year data

Abstract

The model of natural inflation is examined in light of recent 3-year data from the Wilkinson Microwave Anisotropy Probe and shown to provide a good fit. The inflaton potential is naturally flat due to shift symmetries, and in the simplest version takes the form $V(\ensuremath{\phi})={\ensuremath{\Lambda}}^{4}[1\ifmmode\pm\else\textpm\fi{}\mathrm{cos}(N\ensuremath{\phi}/f)]$. The model agrees with WMAP3 measurements as long as $f>0.7{m}_{\mathrm{Pl}}$ (where ${m}_{\mathrm{Pl}}=1.22\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }\text{ }\mathrm{GeV}$) and $\ensuremath{\Lambda}\ensuremath{\sim}{m}_{\mathrm{GUT}}$. The running of the scalar spectral index is shown to be small---an order of magnitude below the sensitivity of WMAP3. The location of the field in the potential when perturbations on observable scales are produced is examined; for $f>5{m}_{\mathrm{Pl}}$, the relevant part of the potential is indistinguishable from a quadratic, yet has the advantage that the required flatness is well-motivated. Depending on the value of $f$, the model falls into the large field ($f\ensuremath{\ge}1.5{m}_{\mathrm{Pl}}$) or small field ($f<1.5{m}_{\mathrm{Pl}}$) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.