The limits of lattice inflation: a cautionary tale
Cosmological lattice simulations have become important tools for studying non-perturbative dynamics in the early Universe. Many widely used codes, however, approximate the gravitational background by an exact Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime and neglect metric perturbations. We show that, during inflation, this approximation prevents the freezing of superhorizon modes. During slow roll, the curvature power spectrum decays as $H^4$, while the deviation becomes substantially stronger during ultra-slow roll. As a result, inflationary observables can be significantly distorted. In contrast, reheating studies appear to be considerably less sensitive to the omission of metric perturbations. We propose a practical criterion for assessing the validity of FLRW simulations based on the inclusion of first-order metric perturbations, and implement it in CosmoLattice.