Linear gravitational waves and electrodynamic formalism in cosmology

The propagation of linear gravitational waves is studied in open and multiply connected Robertson-Walker cosmologies. In order for the group velocity of the gravitational wave packets to coincide with the speed of light, the linear wave equation must be conformally coupled. This opens the possibility of using the electromagnetic formalism. The gravitational analogue to the electromagnetic field tensor is introduced, and a tensorial counterpart to Maxwell's equations on the spacelike 3-slices is derived. The energy-momentum tensor for linear gravitational waves is constructed without averaging procedures, a strictly positive energy density is obtained, and it is shown that the overall energy of a gravitational pulse scales with the inverse of the expansion factor.