Covariant analysis of gravitational waves in a cosmological context

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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 second-order wave equations, for perfect fluids with a -law equation of state satisfying , 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.
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