Constraints on vacuum decay from the microwave background

We consider the possible decay of a vacuum with nonzero energy density into radiation. This is one way to introduce a time-varying cosmological constant, which has been suggested as a means of resolving the cosmological constant problem. We concentrate on the model of Freese et al., in which the vacuum energy density is given as a fraction x/(1 - x) of the energy density of radiation. Using equations for the visible extragalactic background light and assuming that the vacuum decay energy is converted entirely into photons with a Planckian spectrum, we show that the decay process would be capable of contributing significantly to the intensity of the cosmic microwave background. Comparison with COBE observations leads to the constraint x is equal to or less than 0.001, which is stronger than the upper limit of 0.07 obtained previously by Freese et al. from considerations of primordial nucleosynthesis.