  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.
