Covariant analysis of gravitational waves in a cosmological context

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 second-order wave equations, for perfect fluids with a y-law equation of state satisfying 2/3 < y < 2, the electric part of the Weyl tensor satisfies a linear homogeneous third-order equation. Solutions to these equations are obtained for a flat Friedmann-Robertson-Walker background and we discuss implications of this result.