Inhomogeneous Cosmology using General Relativistic Smoothed Particle Hydrodynamics coupled to Numerical Relativity

TL;DR

This paper introduces a coupled numerical relativity and smoothed particle hydrodynamics approach to simulate inhomogeneous cosmologies, accurately capturing linear and non-linear perturbations and dark matter halo formation.

Contribution

It presents a novel method combining numerical relativity with SPH for inhomogeneous cosmology simulations, capable of modeling non-linear effects and structure formation.

Findings

Exact solutions agree with residuals of 10^{-6} and 10^{-3} for dust and radiation.

Linear perturbations evolve with residuals of 10^{-2} compared to exact solutions.

Non-linear metric perturbations enable dark matter halo formation.

Abstract

We perform three-dimensional simulations of homogeneous and inhomogeneous cosmologies via the coupling of a numerical relativity code for spacetime evolution and smoothed particle hydrodynamics (SPH) code. Evolution of a flat dust and radiation dominated Friedmann-Lema\^itre-Roberston-Walker (FLRW) spacetime shows an agreement of exact solutions with residuals on the order $10^{-6}$ and $10^{-3}$ respectively, even at low grid resolutions. We demonstrate evolution of linear perturbations of density, velocity and metric quantities to the FLRW with residuals of only $10^{-2}$ compared to exact solutions. Finally, we demonstrate the evolution of non-linear perturbations of the metric past shell-crossing, such that dark matter halo formation is possible. We show that numerical relativistic smoothed particle hydrodynamics is a viable method for understanding non-linear effects in cosmology.