Non-linear Dynamics and Primordial Curvature Perturbations from Preheating

Understand

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.