Electromagnetic Radiation in Multiply Connected Robertson-Walker Cosmologies

Maxwell's equations on a topologically nontrivial cosmological background are studied. The cosmology is locally determined by a Robertson-Walker line element, but the spacelike slices are open hyperbolic manifolds, whose topology and geometry may vary in time. In this context the spectral resolution of Maxwell's equations in terms of horospherical elementary waves generated at infinity of hyperbolic space is given. The wave fronts are orthogonal to bundles of unstable geodesic rays, and the eikonal of geometric optics appears just as the phase of the horospherical waves. This fact is used to attach to the unstable geodesic rays a quantum mechanical momentum. In doing so the quantized energy-momentum tensor of the radiation field is constructed in a geometrically and dynamically transparent way, without appealing to the intricacies of the second quantization. In particular Planck's radiation formula, and the bearing of the multiply connected topology on the fluctuations in the temperature of the background radiation is discussed.