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

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