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. II. FRAMEWORK AND ADDED-UP PROBABILITY A. Theoretical backgroundThe four-dimensional spatially flat FRW spacetime is described by the metric arXiv:1805.09620v1 [gr-qc]

In the presence of a gravitational field decay rates may significantly differ from flat space equivalent. By studying mutually interacting quantum fields the decay rates can be calculated on a given spacetime. This paper presents the calculation of the transition probability for the decay of a massive scalar particle in a stiff matter dominated universe. We find that due to the precence of a gravitational field a finite correction to the transition probability is added which depends inversely on the mass. Moreover the decay rate is smaller and lifetime of the particles is longer compared to flat space. The mass dependence is such that the lifetime of lighter particles is prolonged more compared to heavier particles. This result may be of significance when studying cosmological situations involving stiff matter.

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 ∼ t, the relative correction term may be of importance.

We present a general model of qubit dynamics which entails pure dephasing and dissipative time-local master equations. This allows us to describe the combined effect of thermalisation and dephasing beyond the usual Markovian approximation. We investigate the complete positivity conditions and introduce a heuristic model that is always physical and provides the correct Markovian limit. We study the effects of temperature on the non-Markovian behaviour of the system and show that the noise additivity property discussed by Yu and Eberly in Ref.[1] holds beyond the Markovian limit.

We provide a detailed study of reheating in the kination regime where particle content is created by gravitational production of massive scalars mutually interacting with a massless scalar field. The produced particles subsequently decay into massless particles eventually reheating the Universe. We aim for a more precise picture using Boltzmann equations and decay rates obtained by methods of quantum field theory in curved spacetime. By numerical calculations it is found that after inflation the Universe ends up being dominated by ordinary matter for a while before the radiation dominated era. The reheating temperature itself is found to be in the 10 6 − 10 12 GeV regime.