Covariant Analysis of Gravitational Waves in a Cosmological Context

TL;DR

This paper investigates the behavior of gravitational waves in a cosmological setting, revealing that different components of the Weyl tensor obey higher-order wave equations depending on the fluid's equation of state.

Contribution

It demonstrates that the electric part of the Weyl tensor satisfies a third order wave equation in a perturbed FRW universe with a perfect fluid, extending previous second order analyses.

Findings

Shear and magnetic Weyl parts satisfy second order wave equations.

Electric Weyl part obeys a third order wave equation for certain fluids.

Solutions are derived for flat FRW backgrounds.

Abstract

The propagation of gravitational waves or tensor perturbations in a perturbed Friedmann-Robertson-Walker universe filled with a perfect fluid is re-examined. It is shown that while the shear and magnetic part of the Weyl tensor satisfy linear, homogeneous {\it second order} wave equations, for perfect fluids with a $\gamma$\hs law equation of state satisfying $\case{2}/{3}<\gamma<2$, the electric part of the Weyl tensor satisfies a linear homogeneous {\it third order} equation. Solutions to these equations are obtained for a flat Friedmann-Robertson-Walker background and we discuss implications of this result.