Natural inflation: Status after WMAP 3-year data

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()=Λ4[1±cos (N/f)]. The model agrees with WMAP3 measurements as long as f>0.7mPl (where mPl=1.22×1019GeV) and Λ∼mGUT. 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>5mPl, 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 ≥ 1.5mPl) or small field (f<1.5mPl) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.