Covariant Analysis of Gravitational Waves in a Cosmological Context

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 $γ$\hs law equation of state satisfying $\case{2}/{3}<γ<2$, 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.