  We derive a curved space generalization of a scalar to fermion decay rate
with a Yukawa coupling in expanding Friedmann-Robertson-Walker universes. This
is done using the full theory of quantum fields in curved spacetime and the
added-up transition probability method. It is found that in an expanding
universe the usual Minkowskian decay rates are considerably modified for early
times. For conformally coupled scalars the decay rate is modified by a positive
additive term proportional to the inverse of mass and related to the expansion
rate of the Universe. We compare and contrast our results with previous studies
on scalar to scalar decay and find that in general the decay channel into
fermions is the dominant channel of decay in the very early Universe.
