Lattice simulations of axion-U(1) inflation

We present the first nonlinear lattice simulation of an axion field coupled to a U(1) gauge field during inflation. We use it to fully characterize the statistics of the primordial curvature perturbation ζ . We find high-order statistics to be essential in describing non-Gaussianity of ζ in the linear regime of the theory. On the contrary, non-Gaussianity is suppressed when the dynamics become nonlinear. This relaxes the bounds from overproduction of primordial black holes, allowing for an observable gravitational waves signal at pulsar timing array and interferometer scales. Our work establishes lattice simulations as a crucial tool to study the inflationary epoch and its predictions.