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.
