  The lack of energy conservation introduces new particle processes in curved
spacetime that are forbidden in flat space. Therefore one has to be very
cautious about using the results calculated in Minkowskian space in early
universe applications. This is true for particle decay rates in particular,
which need to be calculated using quantum field theory in curved spacetime.
Previous studies are usually restricted to using minimal or conformal coupling
for the decaying particle, while using a more general coupling would give
deeper insight into particle decay. This paper presents the results we obtained
for a massive particle decaying in a general power-law universe with arbitrary
coupling to gravity. We find that depending on the value of the gravitational
coupling, the effect of gravitation may either strengthen or weaken the decay.
The analysis further reveals that, apart from radiation dominated universe,
there are values of the coupling constant for which the decay rate is exactly
Minkowskian for all universe types. Because the decay rate may be considerably
modified in curved space, these issues need to be considered when doing precise
cosmological calculations.
