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.

我们通过在扩展的Friedmann–Robertson–Walker宇宙中用Yukawa耦合得出标量到费米子衰减率的弯曲空间泛化。这是使用弯曲时空中的量子场的完整理论和附加的跃迁概率方法完成的。人们发现，在膨胀的宇宙中，通常的Minkowskian衰减率在早期就已大大改变。对于共形耦合标量，衰减率由与质量的反比成正比且与宇宙的膨胀率成正比的正加项来修改。我们将我们的结果与先前关于标量到标量衰变的研究进行比较和对比，发现一般来说，进入费米子的衰变通道是宇宙早期最主要的衰变通道。