A Relativistic view on large scale N-body simulations

TL;DR

This paper explores the connection between Newtonian N-body simulations and General Relativity on large scales, highlighting the accuracy of the Zeldovich approximation and the need to reassess second-order initial conditions.

Contribution

It provides a relativistic perspective on large-scale N-body simulations, emphasizing the limitations of Newtonian approaches and proposing a gauge-based measure for density fluctuations.

Findings

Zeldovich approximation aligns with GR on large scales at leading order.

Second order deviations suggest re-evaluating 2LPT initial conditions.

Synchronous gauge density offers a stable measure of fluctuations.

Abstract

We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large scales, coinciding with the General Relativistic result. At second order in the initial metric potential, the trajectories of particles deviate from the second order Newtonian result and hence the validity of 2LPT initial conditions should be reassessed when used in very large simulations. We also advocate using the expression for the synchronous gauge density as a well behaved measure of density fluctuations on such scales.