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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 thedoi:10.1140/epjc/s10052-020-8074-8 fatcat:jpbvboumtvgbxfddhnysaxgdry