# Production and Backreaction of Fermions from Axion-$SU(2)$ Gauge Fields during Inflation

## TL;DR

This paper investigates fermion production from $SU(2)$ gauge fields and axions during inflation, showing that backreaction effects are negligible for parameters relevant to observations, with new technical methods for calculations.

## Contribution

It introduces improved techniques for calculating fermion production and backreaction in an inflationary $SU(2)$ gauge field-axion system, demonstrating negligible backreaction effects.

## Key findings

- Fermion backreaction on the gauge background is negligible for observational parameters.
- Tree-level backreaction of fermions on gauge fields and axion is very small.
- Loop effects of fermion production are estimated to be insignificant.

## Abstract

$SU(2)$ gauge fields and axions can have a stable, isotropic and homogeneous configuration during inflation. However, couplings to other matter species lead to particle production, which in turn induces backreaction on and destabilization of the non-abelian and axion background. In this paper, we first study the particle production by a $SU(2)$ gauge field coupled to a massive Dirac doublet. To carry out this calculation we have made two technical improvements compared to what has been done in the literature. First, we apply the anti-symmetrization of the operators to treat particles and anti-particles on equal footing, second, to deal with the UV divergences, we apply instantaneous subtraction. We find that, the backreaction of produced fermions on the $SU(2)$ background is negligible for model parameters of observational interest. Next, we consider production of fermions due to coupling to the axion. The tree-level backreaction on the gauge fields, as well as on the axion, is vanishingly small. We also provide an estimate for the loop effects.