Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation

TL;DR

This paper uses nonperturbative lattice simulations to analyze the nonlinear relationship between inflaton field configurations and curvature perturbations in ultra-slow-roll inflation, revealing significant effects on non-Gaussianity and observable predictions.

Contribution

It introduces a nonperturbative $ abla$ approach applied to lattice data to generate fully nonlinear curvature perturbation maps, improving predictions of primordial black holes and gravitational waves.

Findings

Nonlinear mapping enhances the positive tail of the $$ distribution.

Significant non-Gaussianity arises from nonlinear dynamics at Hubble crossing.

Perturbative approaches can break down when fluctuations become large.

Abstract

Building on the recent lattice simulations of ultra-slow-roll (USR) dynamics presented in arXiv:2410.23942, we investigate the role of the nonlinear relation between the inflaton field configuration and the curvature perturbation $\zeta$, the key observable after inflation. Using a nonperturbative $\delta N$ approach applied to the lattice output, we generate fully nonlinear three-dimensional maps of $\zeta$. This calculation captures both the non-Gaussianity arising from the nonlinear mapping between $\phi$ and $\zeta$, and the intrinsic non-Gaussianity generated around Hubble crossing by the nonlinear field dynamics, which is neglected in stochastic approaches. We find that the nonlinear mapping has a profound impact on the statistics, significantly enhancing the positive tail of the $\zeta$ probability distribution, with important implications for observable quantities. A central part of this work is the comparison with the standard perturbative treatment based on a gauge transformation, which allows us to quantify when and how the perturbative picture breaks down as fluctuations grow large. Together with arXiv:2410.23942, this work sets the basis for robust, nonperturbative predictions of primordial black hole production and scalar-induced gravitational wave emission from inflation using lattice simulations.