Does relativistic cosmology software handle emergent volume evolution?

TL;DR

This study evaluates whether relativistic cosmology software accurately models emergent volume evolution by comparing numerical results with exact solutions, confirming the reliability of inhomog and gevolution in specific scenarios.

Contribution

It introduces a method to test the accuracy of relativistic cosmology software in modeling volume evolution using exact perturbed solutions.

Findings

inhomog accurately models emergent volume evolution at first order.

inhomog matches Friedmann solutions within 0.006% for specified initial conditions.

gevolution models decaying modes with high accuracy, excluding growing modes by design.

Abstract

Several software packages for relativistic cosmological simulations that do not fully implement the Einstein equation have recently been developed. Two of the free-licensed ones are inhomog and gevolution. A key question is whether globally emergent volume evolution that is faster than that of a Friedmannian reference model results from the averaged effects of structure formation. Checking that emergent volume evolution is correctly modelled by the packages is thus needed. We numerically replace the software's default random realisation of initial seed fluctuations by a fluctuation of spatially constant amplitude in a simulation's initial conditions. The average volume evolution of the perturbed model should follow that of a Friedmannian expansion history that corresponds to the original Friedmannian reference solution modified by the insertion of the spatially constant perturbation. We derive the equations that convert from the perturbed reference solution to the effective solution. We find that inhomog allows emergent volume evolution correctly at first order through to the current epoch. For initial conditions with a resolution of $N = 128^3$ particles and an initial non-zero extrinsic curvature invariant $I_i = 0.001$, inhomog matches an exact Friedmannian solution to -0.0058% (Einstein-de Sitter, EdS) or -0.0033% (LCDM). We find that gevolution models the decaying mode to fair accuracy, and excludes the growing mode by construction. For $N = 128^3$ and an initial scalar potential $\Phi$ = 0.001, gevolution is accurate for the decaying mode to 0.012% (EdS) or 0.013% (LCDM). We conclude that this special case of an exact non-linear solution for a perturbed Friedmannian model provides a robust calibration for relativistic cosmological simulations.