Metric Perturbation Approach to Gravitational Waves in Isotropic Cosmologies

TL;DR

This paper develops a metric perturbation method for gravitational waves in isotropic cosmologies, aligning with previous gauge-invariant results and enabling comparison with Bardeen's approach.

Contribution

It introduces a linearised metric perturbation framework that reproduces gauge-invariant results and simplifies comparison with alternative methods.

Findings

Successfully reproduces gauge-invariant results for gravitational waves

Provides a straightforward way to compare with Bardeen's approach

Enhances understanding of gravitational wave perturbations in cosmology

Abstract

Gravitational waves in isotropic cosmologies were recently studied using the gauge-invariant approach of Ellis-Bruni. We now construct the linearised metric perturbations of the background Robertson-Walker space-time which reproduce the results obtained in that study. The analysis carried out here also facilitates an easy comparison with Bardeen.