Enhancement of the dark matter abundance before reheating: Applications to gravitino dark matter

In the first stages of inflationary reheating, the temperature of the radiation produced by inflaton decays is typically higher than the commonly defined reheating temperature T-RH similar to (Gamma M-phi(P))(1/2) where Gamma(phi) is the inflaton decay rate. We consider the effect of particle production at temperatures at or near the maximum temperature attained during reheating. We show that the impact of this early production on the final particle abundance depends strongly on the temperature dependence of the production cross section. For similar to T-n/Mn+2, and for n < 6, any particle produced at T-max is diluted by the later generation of entropy near TRH. This applies to cases such as gravitino production in low scale supersymmetric models (n = 0) or NETDM models of dark matter (n = 2). However, for n = 6 the net abundance of particles produced during reheating is enhanced by over an order of magnitude, dominating over the dilution effect. This applies, for instance to gravitino production in high scale supersymmetry models where n = 6.