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According to the standard model of cosmology, the early universe has beendominated by radiation or non-relativistic matter in several eras of itshistory. However, many cosmological calculations involving particle processesare commonly done using Minkowskian results for them, although, for moreprecise treatment, quantum field theory in curved spacetime is needed. Thispaper aims to fill this gap by presenting decay rates for matter and radiationdominated universes in this more precise treatment. We provide a study of theaverage decay rates for a process where a conformally coupled massive scalarfield decays into massless scalar particles. It is found that the presence of acurved spacetime modifies the Minkowskian result considerably for early timesbut asymptotically only by an additive term proportional to the inverse of massand interaction time. Thus, the correction is small for large time scales, buton the time scales of the order of $m\sim t$, the relative correction term maybe of importance.

Decaying Massive Particle in Matter and Radiation Dominated Eras