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

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.