Lattice Simulations of Axion-U(1) Inflation

If gauge fields are coupled to an axion field during inflation, they lead to unique observational signatures within the reach of next generation experiments. However, this system often shows strong backreaction effects, invalidating the standard perturbation theory approach. In this paper, we present the first nonlinear lattice simulation of inflation driven by an axion field coupled to an abelian U(1) field. We use it to fully characterize the statistics of the comoving curvature perturbation $\zeta$. We find that non-Gaussianity of $\zeta$ is large in the linear regime, whereas it is strongly suppressed when the dynamics becomes nonlinear. This relaxes bounds from overproduction of primordial black holes.