Tachyons in the Milne universe

Superluminal particles (tachyons) are studied in a Robertson-Walker cosmology with linear expansion factor and negatively curved 3-space (Milne universe). This cosmology admits globally geodesic rest frames for uniformly moving observers, isometric copies of the forward lightcone, which can be synchronized by Lorentz boosts. We investigate superluminal wave propagation, a real Proca field with negative mass-square, coupled to subluminal matter in analogy to the electromagnetic field. For photons, the eikonal approximation is exact in Robertson-Walker cosmology, and the Proca field is coupled to the background geometry in such a way that this also holds for tachyons. The spectral decomposition of freely propagating tachyon fields in the Milne universe is derived. We study the wave-particle duality in terms of the spectral elementary waves and their orthogonal ray bundles, in the comoving frame as well as in the individual geodesic rest frames of galactic observers. The spectral energy density of a tachyon background radiation is discussed.