Notes on natural inflation

TL;DR

This paper explores a modified model of natural inflation where an axion-like inflaton coupled to Yang-Mills theory exhibits a multi-valued potential, enabling chaotic inflation with sub-Planckian decay constants, supported by supersymmetric analysis.

Contribution

It introduces a new perspective on natural inflation by showing that coupling to Yang-Mills theory results in an effectively quadratic potential, allowing for inflation with smaller decay constants.

Findings

Multi-valued potential becomes effectively quadratic at large N.

Chaotic inflation can occur with decay constants below the Planck scale.

Moderately large gauge groups like E8 are sufficient for this mechanism.

Abstract

In the so-called natural inflation, an axion-like inflaton is assumed to have a cosine-type periodic potential. This is not the case in a very simple model in which the axion-like inflaton is coupled to an SU(N) (or other) pure Yang-Mills, at least in the large N limit as pointed out by Witten. It has a multi-valued potential, which is effectively quadratic, i.e., there is only a mass term in the large N limit. Thanks to this property, chaotic inflation can be realized more naturally with the decay constant of the axion-like inflaton less than the Planck scale. We demonstrate these points explicitly by using softly broken ${\mathcal N}=1$ Super-Yang-Mills which allows us to treat finite N. This analysis also suggests that moderately large gauge groups such as $E_{8}$ are good enough with a Planck scale decay constant.