Axion cosmology with post-Newtonian corrections

TL;DR

This paper develops first-order post-Newtonian approximations for imperfect fluids and axions in cosmology, deriving covariant Schrödinger and hydrodynamic formulations, and analyzing linear instabilities in a gauge-invariant manner.

Contribution

It introduces the first 1PN formulations for axions and imperfect fluids in cosmology, including covariant derivations of Schrödinger and hydrodynamic equations.

Findings

Derived covariant 1PN equations for axions and fluids.

Analyzed gauge-invariant linear instability and static limits.

Provided comprehensive equations without fixing gauge conditions.

Abstract

We present first-order post-Newtonian (1PN) approximations of a general imperfect fluid and of an axion as a coherently oscillating massive scalar field, both in the cosmological context. For the axion, using the Klein transformation and Madelung transformation we derive the Schr\"odinger and Madelung hydrodynamic formulations, respectively, in exact covariant way and to 1PN order. Complete sets of equations for the 1PN formulations are derived without fixing the temporal gauge condition. We study the linear instability in cosmology and a static limit for both fluid and axion; these are presented independently of the gauge condition to 1PN order, thus are naturally gauge-invariant.