Einstein coefficients and equilibrium formalism for tachyon radiation

The spectral energy density of an ideal Bose gas of superluminal particles (tachyons) is derived. To this end, we consider atoms in equilibrium with tachyon radiation, study spontaneous and induced transitions effected by tachyons, calculate the Einstein coefficients, all semiclassically, and obtain, by detailed balancing, the equilibrium distribution of the tachyon gas. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Atomic transitions induced by tachyons are compared to photonic ones, and the tachyonic analog to the photoelectric effect is discussed. The cosmic tachyon background is scrutinized in detail; high- and low-temperature expansions of the internal energy, the entropy, the heat capacities, and the number density are compared with the corresponding quantities of the photon background. The negative mass square in the wave equation changes the frequency scaling in the Rayleigh–Jeans law, and there are also significant changes in the low-temperature regime, in particular in the caloric and thermal equations of state. Quantitative estimates on the tachyon background and on Rydberg transitions induced by tachyon radiation are derived.