Lattice simulations of scalar-induced gravitational waves from inflation

TL;DR

This paper uses lattice simulations to nonperturbatively compute scalar-induced gravitational waves from ultra-slow-roll inflation, revealing significant deviations from semi-analytical predictions especially with large non-Gaussianities.

Contribution

It introduces a fully nonlinear lattice simulation approach to accurately predict SIGWs during USR inflation, surpassing previous linear perturbation methods.

Findings

Semi-analytical predictions are accurate for moderate non-Gaussianity.

Large non-Gaussianities cause significant deviations in GW amplitude and shape.

Nonperturbative methods are essential for reliable SIGW predictions in certain inflation scenarios.

Abstract

Scalar-induced gravitational waves (SIGWs) provide a powerful probe of inflationary dynamics on scales far smaller than those accessible to the cosmic microwave background and large-scale structure. In scenarios with a transient ultra-slow-roll (USR) phase, the curvature power spectrum can be strongly enhanced on small scales, potentially generating an observable stochastic GW background. In this regime, scalar dynamics during inflation can become nonlinear, challenging the validity of standard perturbative predictions. Existing semi-analytical calculations of SIGWs rely on the linear evolution of inflation fluctuations. In this work, we compute SIGWs from USR inflation using lattice simulations. We evolve the inflaton field fully nonlinearly during inflation and extract the curvature perturbation nonperturbatively, then simulate its post-reheating horizon re-entry by evolving the Newtonian potential linearly while retaining the full non-Gaussian structure of the initial conditions for the primordial fluctuations in the tensor source. For moderate non-Gaussianity, the semi-analytical prediction captures the correct order of magnitude of the GW signal but receives important corrections. When inflationary non-Gaussianities are large, it can fail dramatically in both amplitude and spectral shape, independently of the overall size of the tensor power spectrum. Our results show that reliable predictions of SIGWs in such scenarios require nonperturbative control of the inflationary scalar dynamics. The code used for this work is available at https://github.com/caravangelo/inflation-easy.git.