We analyze in detail the perturbative decay of the inflaton oscillating about a generic form of its potential V(ϕ) = ϕ k , taking into account the effects of non-instantaneous reheating. We show that evolution of the temperature as a function of the cosmological scale factor depends on the spin statistics of the final state decay products when k > 2. We also include the inflaton-induced mass of the final states leading to either kinematic suppression or enhancement if the final states are fermionic or bosonic respectively. We compute the maximum temperature reached after inflation, the subsequent evolution of the temperature and the final reheat temperature. We apply our results to the computation of the dark matter abundance through thermal scattering during reheating. We also provide an example based on supersymmetry for the coupling of the inflaton to 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 temperature1/2 where Γ φ 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 σv ∼ T n /M n+2 , and for n < 6, any particle produced at T max is diluted by the later generation of entropy near T RH . 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.

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