Abstract
Particle production via parametric resonance in the early Universe, is a non-perturbative, 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.
Highlights
Of the inflaton [6,7,8,9,10,11,12,13]
The advantage of using our fitted formulas will be twofold: on the one hand skipping the tedious task of running new simulations, and on the other hand preventing the use of over-simplified linear analysis of the problem
The latter is characterized by the different energy fractions of the fields evolving very slowly, while at the same time an equipartition distribution of energies is set. This regime is attained at a time zdec. We consider this moment as the truly decay time scale of the mother field: while during the non-linear regime zbr ≤ z ≤ zdec energy is significantly exchanged between the mother and the daughter fields, at z ≥ zdec the energy exchange ceases and the energy fractions evolve in a stationary regime
Summary
Parametric resonance in the early Universe can be realized in two main different circumstances: i) when the mother field dominates the energy budget of the Universe, and ii) when the mother field is only a sub-dominant energy component of the Universe. In the quadratic model the energy density of the inflaton (again after oscillations-averaging) evolves as in a MD background, with ρφ ∝ 1/a3, and the scale factor evolving correspondingly as a(t) ∼ t2/3. Both scenarios of inflation are challenged by recent CMB measurements [1] (the quartic case more severely), but in reality, the simple addition of an non-minimal gravitational coupling to the inflaton can reconcile these scenarios with the observations [2]. It is interesting to note that this interaction does not lead to a tree level decay of the mother field into the daughter species, so all the transfer of energy from φ into X will be due only to the non-perturbative effects characteristic of parametric resonance
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