Inhomogeneous Cosmology with Numerical Relativity

TL;DR

This paper demonstrates that numerical relativity can accurately simulate the evolution of inhomogeneous cosmological spacetimes, capturing nonlinear effects and bridging linear perturbation theory with fully nonlinear regimes.

Contribution

It introduces a high-precision numerical relativity approach to study nonlinear cosmological inhomogeneities, validating its accuracy against linear solutions and exploring nonlinear effects.

Findings

Achieved fourth-order convergence with errors less than 10^-6.

Found agreement within 10^-3 between numerical and linear solutions.

Simulated the growth of perturbations into the nonlinear regime, revealing effects like gravitational slip.

Abstract

We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble flow over a factor of ~350 change in scale factor (redshift). We simulate the growth of linear perturbations into the non-linear regime, where effects such as gravitational slip and tensor perturbations appear. We therefore show that numerical relativity is a viable tool for investigating nonlinear effects in cosmology.