Cosmological post-Newtonian equations from nonlinear perturbation theory

TL;DR

This paper derives the cosmological first-order post-Newtonian equations from a fully nonlinear perturbation theory, providing a new perspective and comparison between the two approaches for understanding relativistic nonlinear processes in cosmology.

Contribution

It presents a novel derivation of post-Newtonian equations from nonlinear perturbation theory without fixing gauge conditions, enabling better analysis of relativistic effects in structure formation.

Findings

Equations derived without fixing gauge conditions.

Comparison between nonlinear perturbation theory and post-Newtonian approximation.

Framework applicable to relativistic nonlinear cosmological processes.

Abstract

We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.