Newtonian N-body simulations are compatible with cosmological perturbation theory

TL;DR

This paper demonstrates that Newtonian N-body simulations of dark matter are consistent with general relativity at the linear level, validating their use in cosmological studies despite recent claims to the contrary.

Contribution

It clarifies the conditions under which Newtonian simulations align with general relativity, emphasizing the role of gauge-invariant observables and linear perturbation theory.

Findings

Newtonian simulations match GR for linear observables.

Discrepancies on the lightcone are due to gravitational lensing.

Large Hubble fluctuations mainly affect lensing, not simulation validity.

Abstract

Contrary to recent claims in the literature, Newtonian N-body simulations of collisionless Dark Matter in a LambdaCDM background are compatible with general relativity and are not invalidated by general relativistic effects at the linear level. This verdict is based on four facts. (1) The system of linearized Einstein equations and conservation laws is well-posed in the gauge invariant formulation and physically meaningful. (2) Comparing general relativity with its Newtonian approximation at a given order in perturbation theory is only meaningful at the level of observables. (3) The dynamics of observables describing a dust fluid in general relativity and its Newtonian approximation agree at the linear level. Any disagreement for observables on the lightcone are well-known, of which the most dominant is gravitational lensing. (4) Large fluctuations in the Hubble parameter contribute significantly only to gravitational lensing effects. Therefore, these fluctuations are not in conflict with Newtonian N-body simulations beyond what has already been carefully taken into account using ray tracing technology.