Newtonian, post-Newtonian and Relativistic Cosmological Perturbation Theory

TL;DR

This paper derives a comprehensive set of relativistic cosmological perturbation equations valid to full nonlinear order, extending Newtonian and post-Newtonian frameworks without fixing a gauge, and includes pressure correction terms.

Contribution

It provides the first fully nonlinear relativistic cosmological perturbation equations without gauge fixing, bridging Newtonian, post-Newtonian, and relativistic regimes.

Findings

Relativistic equations reduce to Newtonian and post-Newtonian limits.

Includes relativistic pressure correction terms in Newtonian hydrodynamics.

Provides gauge-independent formulation of nonlinear perturbation theory.

Abstract

Newtonian cosmological perturbation equations valid to full nonlinear order are well known in the literature. Assuming the absence of the transverse-tracefree part of the metric, we present the general relativistic counterpart valid to full nonlinear order. The relativistic equations are presented without taking the slicing (temporal gauge) condition. The equations do have the proper Newtonian and first post-Newtonian limits. We also present the relativistic pressure correction terms in the Newtonian hydrodynamic equations.