A numerical relativity scheme for cosmological simulations

TL;DR

This paper introduces a new 3+1 numerical relativity scheme for cosmological simulations that simplifies the equations by removing fluid components via constraints, applicable in arbitrary gauges and equations of state.

Contribution

It presents a novel unconstrained evolution scheme for General Relativity in cosmology that eliminates fluid variables through constraints, enhancing flexibility and robustness.

Findings

Scheme works in arbitrary gauge and equation of state

Allows for a cosmological adaptation of the robustness test

Applicable to pressureless perfect fluids in late-time cosmology

Abstract

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3+1 integration scheme for General Relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.