On: Natural Inflation

TL;DR

Re-examines Natural Inflation with a PNGB inflaton and a cosine-type potential, arguing that a flat potential can arise from shift symmetry and that the model remains viable for f around the Planck scale. The analysis combines slow-roll and exact numerical evolution, showing that sufficient inflation is achieved for f ≳ 0.06 m_Pl and that realistic Λ ≈ m_GUT yields the observed density perturbations. The model predicts a tensor component r that could be detectable by Planck for f ≳ 1.5 m_Pl (and by future experiments down to f ≈ 0.7 m_Pl), while the running of the scalar index is negligible. These results place Natural Inflation as a testable, symmetry-protected mechanism for flat potentials in the early universe.

Abstract

We re-examine the original model of Natural inflation, in which the inflaton is a pseudo Nambu-Goldstone boson with potential of the form $ V(φ) = Λ^4 [1 \pm \cos(φ/f)]$, in light of recent data. We find that the model is alive and well. Successful inflation as well as recent data from the Wilkinson Microwave Anisotropy probe require $f > 0.6 m_{\rm Pl}$ (where $m_{\rm Pl} = 1.22 \times 10^{19}$ GeV) and $Λ\sim m_{GUT}$, scales which can be accommodated in particle physics models. The detectability of tensor modes from natural inflation in upcoming microwave background experiments is discussed. We find that natural inflation predicts a tensor/scalar ratio within reach of future observations.

Figures (1)

• Figure 1: The predictions of Natural Inflation compared with current and projected observational constraints, plotted on the $(r,n_s)$ plane, where $r$ is the tensor/scalar ratio and $n_s$ is the spectral index of scalar fluctuations. The lines show the predictions of natural inflation for varying choices of the mass scale $f$ and the number of e-folds $N_I$. Length scales of order the current horizon size correspond to $N_I \simeq 60$ for high reheat temperature. In general, a lower value of $f$ results in a "redder" (smaller $n_s$) spectrum and a smaller tensor fluctuation amplitude. The shaded region at the left of the plot (green) is excluded to $2\sigma$ by WMAP will2. The hatched (blue) error ellipse is the $2 \sigma$ sensitivity expected for the Planck satellite. The central value is arbitrary: only the size of the error bar is significant. The solid (black) error ellipse is the corresponding result for a hypothetical experiment with the same angular resolution as Planck but with a factor of three better temperature sensitivity. Such a measurement would be capable of detecting the gravitational wave fluctuations from Natural Inflation.