A universal constraint on axion non-Abelian dynamics during inflation

Inflationary models equipped with Chern-Simons coupling between their axion and gauge sectors exhibit an array of interesting signals including a testable chiral gravitational wave spectrum. The energy injection in the gauge sector triggered by the rolling axion leads to a well-studied enhancement of gauge field fluctuations. These may in turn affect observables such as the scalar and tensor spectra and also account for non-linear corrections to field propagators. In this work, we focus on non-Abelian gauge sectors. We show that gauge field self-interactions and axion-gauge field non-linear couplings significantly renormalize the gauge field mode function. Operating within the regime of validity of the perturbative treatment places strong constraints on the accessible parameter space of this class of models. We calculate corrections to the gauge field propagator that are universally present in these scenarios. Enforcing perturbativity on such propagators leads to bounds that are competitive with those stemming from analytical estimates on the onset of the strong backreaction regime.