Stochastic Inflation in Numerical Relativity

TL;DR

This paper develops and implements gauge-invariant stochastic inflation equations within Numerical Relativity, demonstrating their robustness and applicability to complex inflationary scenarios with non-linear dynamics.

Contribution

It re-derives stochastic inflation equations in a gauge-invariant form and presents their successful numerical implementation in the BSSN framework, enabling non-perturbative cosmological simulations.

Findings

Numerical simulations accurately reproduce the evolution of all dynamical variables.

Energy and momentum constraints are well-satisfied in the simulations.

The approach is applicable to both slow-roll and ultra slow-roll inflation scenarios.

Abstract

A set of 3+1 equations for stochastic inflation incorporating all metric and scalar matter degrees of freedom, first presented in previous work, are re-derived in a gauge invariant manner. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of Numerical Relativity, demonstrating their efficacy in both a slow-roll and an ultra slow-roll scenario. We find the evolution is correctly reproduced for all the dynamical variables, and the energy and momentum constraints are well-satisfied. This demonstrates that the stochastic equations are theoretically and numerically robust and ready to be applied to a wider inflationary landscape. Our simulations result in real space realizations of the fully non-linear stochastic dynamics with \new{gradients and anisotropic expansion retained. This work generalizes standard stochastic inflation, inflationary numerical relativity and lattice cosmology, opening up the possibility for reliable predictions of non-perturbative phenomena and providing} precise initial conditions for subsequent cosmological eras.