Natural Inflation: the status after WMAP 3-year data

TL;DR

Natural Inflation, with a shift-symmetry-driven flat potential, fits WMAP3 data well for certain parameter ranges, and its predictions include small spectral index running and distinguishable large/small field regimes.

Contribution

This paper evaluates Natural Inflation against WMAP3 data, confirming its viability and clarifying the parameter space where it aligns with observations.

Findings

Fits WMAP3 data for f > 0.7 m_{Pl}

Small running of spectral index, below WMAP3 sensitivity

Distinguishable large and small field regimes

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 $V(\phi) = \Lambda^4 [1 \pm \cos(N\phi/f)]$. The model agrees with WMAP3 measurements as long as $f > 0.7 m_{Pl}$ (where $m_{Pl} = 1.22 \times 10^{19}$GeV) and $\Lambda \sim m_{GUT}$. 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 $f > 5 m_{Pl}$, 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 ($f \ge 1.5 m_{Pl}$) or small field ($f < 1.5 m_{Pl}$) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.