Connection between Newtonian simulations and general relativity

TL;DR

This paper demonstrates that Newtonian N-body simulations can accurately model large-scale cosmological structures within general relativity, providing formulas to translate simulation outputs into observable quantities.

Contribution

It establishes the validity of Newtonian simulations for large-scale structures and introduces formulas to connect simulation data with relativistic gauge and observable coordinates.

Findings

Simulations correctly solve dynamics for long modes in general relativity.

Formulas provided to convert simulation positions to conformal Newtonian gauge.

Methods to translate simulation outputs into observable coordinates.

Abstract

On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and velocities in a specific coordinate system or gauge. The method of choice for simulating large-scale structure is numerical N-body simulations which are performed in the Newtonian limit. Even though one might worry that the use of the Newtonian approximation would make it impossible to use these simulations to compute properties on very large-scales, we show that the simulations are still solving the dynamics correctly even for long modes and we give formulas to obtain the position of particles in the conformal Newtonian gauge given the positions computed in the simulation. We also give formulas to convert from the output coordinates of N-body simulations to the observable coordinates of the particles.