Perturbative limits on axion-SU(2) gauge dynamics during inflation from the energy density of spin-2 particles

TL;DR

This paper analyzes when perturbation theory fails in axion-SU(2) gauge systems during inflation due to spin-2 particle energy density, highlighting the need for non-perturbative methods like lattice simulations.

Contribution

It identifies the conditions under which perturbative approaches break down in axion-SU(2) inflation models, emphasizing the importance of non-perturbative techniques.

Findings

Perturbation theory fails when spin-2 energy density exceeds background energy density.

Breakdown occurs near the strong backreaction regime, but can also happen earlier.

Non-perturbative methods are necessary for accurate analysis in these regimes.

Abstract

We investigate the conditions under which the perturbative treatment of the backreaction of spin-2 particles on the dynamics of an axion-SU(2) gauge field system breaks down during cosmic inflation. This condition is based on the ratio of the energy density of spin-2 particles from the SU(2) gauge field to that of the background field. The perturbative treatment breaks down when this ratio exceeds unity. We show that this occurs within a parameter space nearly identical to the strong backreaction regime identified in previous studies. However, in some cases, the ratio exceeds unity even before the system enters the strong backreaction regime. Our results suggest that attempts to study the strong backreaction regime using perturbation theory are necessarily limited. Reliable calculations require non-perturbative treatments, such as three-dimensional lattice simulations.