Non-linear Dynamics and Primordial Curvature Perturbations from Preheating

TL;DR

This paper reviews the non-linear dynamics of preheating after inflation, focusing on how it can generate observable primordial curvature perturbations and discussing numerical methods and simulation results.

Contribution

It introduces a simple method to evaluate Floquet exponents and provides detailed simulations of preheating in chaotic inflation models, highlighting its role in primordial perturbations.

Findings

Preheating involves explosive decay of the inflaton via broad parametric resonance.

Simulations show non-equilibrium transitions, defect formation, and turbulence.

Preheating can produce large-scale non-Gaussian curvature fluctuations observable in CMB.

Abstract

In this paper I review the theory and numerical simulations of non-linear dynamics of preheating, a stage of dynamical instability at the end of inflation during which homogeneous inflaton explosively decays and deposits its energy into excitation of other matter fields. I focus on preheating in chaotic inflation models, which proceeds via broad parametric resonance. I describe a simple method to evaluate Floquet exponents, calculating stability diagrams of Mathieu and Lame equations describing development of instability in $m^2\phi^2$ and $\lambda\phi^4$ preheating models. I discuss basic numerical methods and issues, and present simulation results highlighting non-equilibrium transitions, topological defect formation, late-time universality, turbulent scaling and approach to thermalization. I explain how preheating can generate large-scale primordial (non-Gaussian) curvature fluctuations manifest in cosmic microwave background anisotropy and large scale structure, and discuss potentially observable signatures of preheating.