On the necessity of the revisions for the cosmological matter perturbations from the general relativity

TL;DR

This paper derives exact general relativistic corrections to matter perturbation equations in the $$CDM model, showing their significance in the radiation-dominant era but not in the matter-dominant era.

Contribution

It provides explicit calculations of metric perturbation theory corrections, clarifying when Newtonian approximations are valid in cosmological perturbation analysis.

Findings

Newtonian-based equations are valid in the small scale, matter-dominant era.

Relativistic corrections are significant during the radiation-dominant era.

Corrections are negligible in the matter-dominant era.

Abstract

The differential equations, which are used for matter perturbations, are usually derived from the Newton gravity and the Euler equation in the expanded universe. In this paper, by the explicit calculations of metric perturbation theory in $\Lambda$CDM model, we derive the general relativistic corrections exactly for the equations and show that the differential equations derived from the Newton gravity and the Euler equation are valid in the small scale region from non-relativistic matter dominant era onwards. However the corrections are not negligible in radiation dominant era.