Ultraslow-roll inflation on the lattice: Backreaction and nonlinear effects

Scenarios like $u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}w\ensuremath{-}r\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l$ Inflation significantly change the final stages of slow-roll inflation to create large curvature perturbations that produce gravitational waves (GW) and primordial black holes (PBH). These phases are outside the usual perturbative regime and the authors use lattice simulations to classify nonlinear effects and the backreaction on the background spacetime in ultraslow-roll Inflation. They show that the nonlinear effects introduce corrections around $20$%, which indicates that perturbation theory is not completely invalidated. However, the corrections are important to obtain correct PBH production rates and GW signals.