Gravitational reheating through conformally coupled superheavy scalar particles

We calculate the number density and the energy density of a massive scalar particle conformally coupled to gravity produced by gravitational particle creation in the case the kination stage follows inflation. In this model, mode functions are derived in terms of exact or numerical solutions for the equation of motion without using the perturbative expansion. We define the adiabatic vacuum in each stage and calculate the produced number density and the energy density. The resultant power spectra show that even the superheavy particle which is as heavy as or much heavier than the Hubble scale during inflation can be produced abundantly if the transition time scale from inflation to the kination stage is smaller than the inverse of the mass of the scalar field. We also give simple forms of the reheating temperature for two cases, one that the produced scalar particles decay instantly and the other that they decay when their energy density exceeds that of inflaton.