Gravitational Wave Propagation in Isotropic Cosmologies

TL;DR

This paper investigates how gravitational waves propagate through isotropic cosmological models, emphasizing the role of anisotropic stresses and providing explicit shear-free wave examples similar to electromagnetic Bateman waves.

Contribution

It introduces explicit models of gravitational waves in isotropic cosmologies with anisotropic stresses, highlighting the importance of these stresses for wave propagation.

Findings

Anisotropic stresses are essential for certain gravitational wave solutions.

Constructed explicit shear-free wave examples analogous to electromagnetic Bateman waves.

Demonstrated that gravitational waves can carry arbitrary information in isotropic backgrounds.

Abstract

We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory.