Axion Inflation: Perturbative control in the strong backreaction regime

We study the strong backreaction regime in axion inflation, in which the friction from Abelian gauge fields generated via the pseudo-scalar interaction $\frac{\beta}{4 M_p} \phi F {\tilde F}$ is comparable to Hubble friction. The non-linear dynamics associated with the gauge fields render this regime phenomenologically particularly interesting, but also notoriously difficult to study with perturbative methods. Quantifying the perturbative control through the direct impact on the spectral backreaction using (i) a first-order gradient-expansion formalism including axion gradients, and (ii) a one-loop in-in calculation, we discover an extended mild backreaction regime at large couplings $\beta$, with a relatively large, nearly constant particle production parameter $\xi$. In passing, we point out that CMB non-Gaussianity bounds impose a general upper limit on the product of axion gauge field coupling and Hubble parameter during inflation, $\beta H/M_p < 1.4\cdot 10^{-3}$, independently of the choice of the axion potential.