Decay of the Cosmic Vacuum Energy

Abstract: In his 2005 review, Gravity and the Thermodynamics of Horizons, Paddy suggested that a vacuum in thermal equilibrium with a bath of radiation should have a gradually diminishing energy. We work through the consequences of this scenario, and find that a coupling between the vacuum and a bath of black-body radiation at the temperature of the horizon requires the Hubble rate, $H$, to approach the same type of evolution as in the "intermediate inflation" scenario, with $H\propto t^{-1/3}$, rather than as a constant. We show that such behaviour does not conflict with observations when the vacuum energy is described by a slowly-rolling scalar field, and when the fluctuations in the scalar field are treated as in the "warm inflation" scenario. It does, however, change the asymptotic states of the universe. We find that the existence of the radiation introduces a curvature singularity at early times, where the energy densities in both the radiation and the vacuum diverge. Furthermore, we show that the introduction of an additional non-interacting perfect fluid into the space-time reveals that radiation can dominate over dust at late times, in contrast to what occurs in the standard cosmological model. Such a coupling can also lead to a negative vacuum energy becoming positive.