Decaying Massive Particle in Matter and Radiation Dominated Eras

According to the standard model of cosmology, the early universe has been dominated by radiation or non-relativistic matter in several eras of its history. However, many cosmological calculations involving particle processes are commonly done using Minkowskian results for them, although, for more precise treatment, quantum field theory in curved spacetime is needed. This paper aims to fill this gap by presenting decay rates for matter and radiation dominated universes in this more precise treatment. We provide a study of the average decay rates for a process where a conformally coupled massive scalar field decays into massless scalar particles. It is found that the presence of a curved spacetime modifies the Minkowskian result considerably for early times but asymptotically only by an additive term proportional to the inverse of mass and interaction time. Thus, the correction is small for large time scales, but on the time scales of the order of $m\sim t$, the relative correction term may be of importance.