(With Keith Olive (Minnesota), Yann Mambrini (IJCLab) and Kunio Kaneta (KIAS))
We currently study the perturbative decay of the inflaton as it oscillates about its minumum, assuming the small-field limit of its potential has the form $V(\Phi) = |\Phi|^k$. By keeping track of the non-instantaneous decay, the evolution of effective masses, and the dependence of the decay rate on the final state, we compute the evolution of the instantaneous temperature during reheating, and the production rate of dark matter at the early stages of reheating. So far results are only available for the decay of the inflaton into a pair of fermions. Non-trivial effects arise for both freeze-in and freeze-out dark matter production mechanisms.
In the future we will look at the effect of thermal corrections on rates, the thermalization of the decay products, and non-adiabatic, non-perturbative particle production. In the context of UV-dominated dark matter freeze-in models, these effects have not yet been considered for non-quadratic potentials.