Gravitational Waves in a Spatially Closed deSitter Spacetime

TL;DR

This paper investigates the evolution of gravitational wave perturbations in a maximally extended, spatially closed deSitter universe, deriving equations and solutions for different wave geometries to understand their behavior.

Contribution

It provides a detailed derivation of weak field equations for tensor perturbations in a closed deSitter background and presents solutions for planar and spherical gravitational waves.

Findings

Derived general weak field equations for tensor perturbations.

Obtained explicit solutions for planar and spherical gravitational waves.

Discussed the implications of wave behavior in a closed deSitter universe.

Abstract

Perturbation of gravitational fields may be decomposed into scalar,vector and tensor components.In this paper we concern with the evolution of tensor mode perturbations in a spatially closed deSitter background of RW form. It may be thought as gravitional waves in a classical description. The chosen background has the advantage of to be maximally extended and symmetric. The spatially flat models commonly emerge from inflationary scenarios are not completely extended.We first derive the general weak field equations.Then the form of the field equations in two special cases, planar and spherical waves are obtained and their solutions are presented. We conclued with discussing the significance of the results and their implications.