Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity

TL;DR

This paper demonstrates the use of Numerical Relativity to simulate inhomogeneous inflationary dynamics with realistic initial conditions, capturing both linear and non-linear effects in various inflationary models.

Contribution

It introduces a method to set stochastic initial conditions consistent with the Bunch-Davies vacuum in Numerical Relativity for inflation, enabling fully non-linear simulations of early universe dynamics.

Findings

Standard perturbation theory predictions are recovered for small perturbations.

Non-linear inhomogeneities are quantified in strong resonance models.

The approach enables realistic non-perturbative simulations of inflationary scenarios.

Abstract

We show that it is possible to simulate realistic inhomogeneities during cosmological inflation with high precision using {Numerical Relativity}. Stochastic initial conditions are set in line with the Bunch-Davies {vacuum} and satisfy the Hamiltonian and Momentum constraints of General Relativity to leading order in perturbation theory. The subsequent fully non-linear dynamical evolution is formulated within a family of geodesic gauges but can in principle be adapted to any choice of coordinates. We present 3 examples of inflationary dynamics: a simple quadratic potential, a potential with an inflection point and a strong resonance model. When perturbations are small, we recover standard predictions of cosmological perturbation theory, and we quantify strongly non-linear inhomogeneities when non-perturbative configurations emerge, such as in the strong resonance model. Our results pave the way towards the first realistic non-perturbative, and fully non-linear Numerical Relativity simulations of the early inflationary universe.