# Parametric resonance in the early Universe—a fitting analysis

## 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.

- Authors:

- Theoretical Physics Department, CERN, Geneva (Switzerland)
- Instituto de Física Teórica IFT-UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22680051

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPUTERIZED SIMULATION; COUPLING; EQUILIBRIUM; EVOLUTION; EXPANSION; FIELD THEORIES; HIGGS BOSONS; HIGGS MODEL; INFLATONS; NONLINEAR PROBLEMS; PARTICLE DECAY; PARTICLE PRODUCTION; RELAXATION; RESONANCE; STANDARD MODEL; UNIVERSE

### Citation Formats

```
Figueroa, Daniel G., and Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es.
```*Parametric resonance in the early Universe—a fitting analysis*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/02/001.

```
Figueroa, Daniel G., & Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es.
```*Parametric resonance in the early Universe—a fitting analysis*. United States. doi:10.1088/1475-7516/2017/02/001.

```
Figueroa, Daniel G., and Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es. Wed .
"Parametric resonance in the early Universe—a fitting analysis". United States.
doi:10.1088/1475-7516/2017/02/001.
```

```
@article{osti_22680051,
```

title = {Parametric resonance in the early Universe—a fitting analysis},

author = {Figueroa, Daniel G. and Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es},

abstractNote = {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.},

doi = {10.1088/1475-7516/2017/02/001},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 02,

volume = 2017,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}