General relativistic effects on non-linear power spectra

TL;DR

This paper investigates the impact of general relativistic non-linearities on cosmological power spectra and finds these effects are negligibly small, supporting the continued use of Newtonian approximations in non-linear cosmology.

Contribution

It provides a detailed analysis showing that relativistic corrections to non-linear power spectra are negligible, validating Newtonian methods in cosmological modeling.

Findings

Relativistic corrections are negligibly small across all scales.

Newtonian cosmology remains valid in non-linear regimes.

Supports the use of Newtonian approximations in standard cosmology.

Abstract

Non-linear nature of Einstein equation introduces genuine relativistic higher order corrections to the usual Newtonian fluid equations describing the evolution of cosmological perturbations. We study the effect of such novel non-linearities on the next-to-leading order matter and velocity power spectra for the case of pressureless, irrotational fluid in a flat Friedmann background. We find that pure general relativistic corrections are negligibly small over all scales. Our result guarantees that, in the current paradigm of standard cosmology, one can safely use Newtonian cosmology even in non-linear regimes.