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