Natural inflation: Status after WMAP three-year data

Inflationary cosmology, a period of accelerated expansion in the early Universe, is being tested by cosmic microwave-background measurements. Generic predictions of inflation have been shown to be correct, and in addition individual models are being tested. The model of natural inflation is examined in light of recent three-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 is V(φ) = Λ [1 ± cos(Nφ/f)]. The model agrees with WMAP3 measurements as long as f > 0.7 mPl (where mPl = 1.22 × 10 GeV) 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 > 5 mPl, 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 < 1.5 mPl) or small field (f < 1.5 mPl) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.