Production of massive particles during reheating

What is commonly called the reheat temperature, $T_{RH}$, is not the maximum temperature obtained after inflation. The maximum temperature is, in fact, much larger than $T_{RH}$. As an application of this we consider the production of massive stable dark-matter particles of mass $M_X$ during reheating, and show that their abundance is suppressed as a power of $T_{RH}/M_X$ rather than $\exp(-M_X/T_{RH})$. We find that particles of mass as large as $2\times 10^3$ times the reheat temperature may be produced in interesting abundance. In addition to dark matter, our analysis is relevant for baryogenesis if the baryon asymmetry is produced by the baryon (or lepton) number violating decays of superheavy bosons, and also for relic ultra-high energy cosmic rays if decays of superheavy particles are responsible for the highest energy cosmic rays.