Gravitational waves in cosmological models of Ho\v{r}ava-Witten theory

TL;DR

This paper investigates gravitational wave behavior and backreaction effects in five-dimensional Hořava-Witten cosmological models with expanding and contracting branes, revealing stability differences and backreaction impacts on bulk and brane geometries.

Contribution

It provides a detailed analysis of gravitational wave mode functions and backreaction effects in two specific cosmological solutions of Hořava-Witten theory, highlighting stability and geometric alterations.

Findings

Mode functions are spatially similar but temporally different for the two solutions.

The $(rrow)$ solution's bulk geometry is unstable against backreaction.

Backreaction significantly alters the brane's intrinsic geometry in the $(rrow)$ solution.

Abstract

We study the behavior of gravitational waves and their backreaction on the background in cosmological solutions of the five-dimensional Ho\v{r}ava-Witten theory. As a dynamical background, we consider two cosmological solutions with spatially flat expanding FRW branes, called $(\uparrow)$- and $(\downarrow)$-solutions, in which the orbifold size increases and decreases in time, respectively. % For these background solutions, the wave equation for the tensor perturbation can be solved by the method of separation of variables, and the mode functions are classified by a separation constant which can be regarded as a graviton mass. We show that the spatial behavior of the mode functions are the same for both background solutions, but the temporal behavior is significantly different. We further show that for the $(\uparrow)$ solution, the background bulk geometry is unstable against the backreaction of the perturbation, while for the $(\downarrow)$ solution, the backreaction on the bulk geometry can be neglected. We also show that, in contrast to the effect to the bulk geometry, the backreaction of the perturbation significantly alters the intrinsic geometry of the brane for the $(\downarrow)$ solution.