# General Relativistic Cosmological N-body Simulations I: time integration

## TL;DR

This paper introduces a stable numerical scheme for fully general-relativistic N-body simulations in cosmology, capable of accurately evolving inhomogeneous structures on small scales while maintaining physical constraints.

## Contribution

It presents a novel combination of numerical relativity methods and time-integration algorithms tailored for cosmological N-body simulations, ensuring stability and accuracy in highly inhomogeneous regimes.

## Key findings

- Successfully passes robustness tests
- Accurately follows scalar linear modes in an expanding universe
- Maintains constraint and energy-momentum conservation at small scales

## Abstract

This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization method and time-integration algorithm that provides satisfyingly stable evolution. More precisely, we show that it is able to pass a robustness test and to follow scalar linear modes around an expanding homogeneous and isotropic space-time. Most importantly, it is able to evolve typical cosmological initial conditions on comoving scales down to tenths of megaparsecs with controlled constraint and energy-momentum conservation violations all the way down to the regime of strong inhomogeneity.