Parametric resonance in the early Universe—a fitting analysis

Particle production via parametric resonance in the early Universe, is a nonperturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3 + 1 dimensions, we parametrize the dynamics outcome scanning over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.