On the Transverse-Traceless Projection in Lattice Simulations of Gravitational Wave Production

TL;DR

This paper develops a consistent lattice-based method for extracting the transverse-traceless part of metric perturbations in gravitational wave simulations, confirming previous results are reliable despite earlier concerns about methodological inconsistencies.

Contribution

It introduces a new lattice-compatible prescription for TT projection in gravitational wave simulations, ensuring accurate spectra extraction during (p)reheating.

Findings

Lattice-based TT projection yields similar GW spectra to continuum-based methods.

The new method confirms the reliability of previous GW predictions in lattice simulations.

Differences in amplitude and shape are marginal between the two approaches.

Abstract

It has recently been pointed out that the usual procedure employed in order to obtain the transverse-traceless (TT) part of metric perturbations in lattice simulations was inconsistent with the fact that those fields live in the lattice and not in the continuum. It was claimed that this could lead to a larger amplitude and a wrong shape for the gravitational wave (GW) spectra obtained in numerical simulations of (p)reheating. In order to address this issue, we have defined a consistent prescription in the lattice for extracting the TT part of the metric perturbations. We demonstrate explicitly that the GW spectra obtained with the old continuum-based TT projection only differ marginally in amplitude and shape with respect to the new lattice-based ones. We conclude that one can therefore trust the predictions appearing in the literature on the spectra of GW produced during (p)reheating and similar scenarios simulated on a lattice.