Gravitational Waves in a Closed Spacetime via Deviation Equation

TL;DR

This paper derives the properties of gravitational waves in a closed universe, showing how the cosmological constant influences them mainly in the early universe and proposing a method to use GW damping to probe large-scale curvature.

Contribution

It provides a novel analysis of gravitational waves in a closed spacetime using the deviation equation, highlighting the cosmological constant's role and potential observational implications.

Findings

GW amplitude and frequency depend on discrete wave numbers and cosmological constant

Cosmological constant effects on GWs are significant only in the early universe

Universe expansion causes damping of GWs, useful for characterizing curvature

Abstract

Within the closed universe, we obtain the amplitude and frequency of gravitational waves in the terms of discrete wave numbers, wave propagation time, and cosmological constant using the deviation equation in the first-order perturbed metric. We demonstrate that the cosmological constant effect on GWs is only seen in the early universe. Also, by considering the time evolution of a gravitational wave in a closed spacetime, we investigate its effect on a circle of nearby massless particles, which will be compared with this case in the flat spacetime. Expanding the universe has effective damping on GWs; thus, we suggest it can be used as a tool to characterize the large-scale curvature of the universe