Spinodal Instabilities and Super-Planckian Excursions in Natural Inflation

TL;DR

This paper demonstrates that spinodal instabilities in Natural Inflation models can enable sufficient inflation with sub-Planckian decay constants, potentially avoiding issues with higher-dimensional operators and maintaining observational consistency.

Contribution

It introduces a mechanism where spinodal instabilities modify inflaton dynamics, allowing Natural Inflation to work with decay constants below the Planck scale.

Findings

Natural Inflation can achieve sufficient e-folds with f < M_pl due to instabilities.

Two inflation phases emerge, driven by zero mode and unstable modes.

Tensor-to-scalar ratio r is typically very small, making it observationally elusive.

Abstract

Models such as Natural Inflation that use Pseudo-Nambu-Goldstone bosons (PNGB's) as the inflaton are attractive for many reasons. However, they typically require trans-Planckian field excursions $\Delta \Phi>M_{\rm Pl}$, due to the need for an axion decay constant $f>M_{\rm Pl}$ to have both a sufficient number of e-folds {\em and} values of $n_s,\ r$ consistent with data. Such excursions would in general require the addition of all other higher dimension operators consistent with symmetries, thus disrupting the required flatness of the potential and rendering the theory non-predictive. We show that in the case of Natural Inflation, the existence of spinodal instabilities (modes with tachyonic masses) can modify the inflaton equations of motion to the point that versions of the model with $f<M_{\rm Pl}$ can still inflate for the required number of e-folds. The instabilities naturally give rise to two separate phases of inflation with different values of the Hubble parameter $H$ one driven by the zero mode, the other by the unstable fluctuation modes. The values of $n_s$ and $r$ typically depend on the initial conditions for the zero mode, and, at least for those examined here, the values of $r$ tend to be unobservably small.