Fully-relativistic evolution of vacuum tensor inhomogeneities during inflation

TL;DR

This paper develops a comprehensive relativistic simulation method for inflationary tensor perturbations, enabling detailed analysis of gravitational effects and non-Gaussian features relevant for future CMB observations.

Contribution

It introduces a novel approach to initialize and extract inflationary tensor perturbations in fully relativistic simulations, bridging perturbation theory and numerical relativity.

Findings

Validated the method against linear solutions with high accuracy.

Demonstrated preservation of energy and momentum constraints to second order.

Provided initial results on tensor non-Gaussianity measures.

Abstract

We present a complete method for the initialisation and extraction of first-order inflationary tensor perturbations for fully relativistic simulations which incorporate gravitational back-reaction. We outline a correspondence between the Cosmological Perturbation Theory (CPT) framework and the numerical relativity BSSN variables in the appropriate limit. We describe a generation method for stochastic tensoral initial conditions, inspired by the standard scalar initial condition used from inflation and implemented in lattice cosmology. We discuss the implementation of this procedure in the GRChombo/GRTeclyn code, and demonstrate the detailed quantitative correspondence between the linearised and fully-nonlinear solutions in the perturbative limit, through the evolution of the background and the tensor power spectrum. We also validate the methodology by showing that energy and momentum constraints are introduced and preserved to second-order or better. We provide some preliminary indicative results probing tensoral non-Gaussianity using the skewness and kurtosis. The computational pipeline presented here will be used to study the emergence of a primordial tensor bispectra and cross-spectra that incorporate the effect of nonlinear gravitational couplings with the metric, which has potential applications for the analysis of next-generation CMB surveys.