Backreaction for Einstein-Rosen waves coupled to a massless scalar field

TL;DR

This paper introduces an exact solution involving Einstein-Rosen waves coupled to a scalar field to analyze the Green-Wald backreaction framework, demonstrating its unique determination of backreaction and consistency with other methods.

Contribution

It provides a new explicit solution to study the Green-Wald backreaction framework and compares its results with existing approaches, confirming their agreement.

Findings

Green-Wald framework uniquely determines backreaction for finite inhomogeneities.

Results align with Charach-Malin and Isaacson methods in the vacuum limit.

The solution models a generalized Gowdy cosmology with scalar and gravitational waves.

Abstract

We present a one-parameter family of exact solutions to Einstein equations that may be used to study the nature of the Green-Wald backreaction framework. Our explicit example is a family of Einstein-Rosen waves coupled to a massless scalar field. This solution may be reinterpreted as a generalized three-torus polarized Gowdy cosmology with scalar and gravitational waves. We use it to illustrate essential properties of the Green-Wald approach. Among other things we show that within our model the Green-Wald framework uniquely determines backreaction for finite size inhomogeneities on a predefined background. The results agree with those calculated in the Charach-Malin approach. In the vacuum limit, the Green-Wald, the Charach-Malin and the Isaacson method imply identical backreaction as expected.