In this paper I review the theory and numerical simulations of nonlinear dynamics of preheating, a stage of dynamical instability at the end of inflation during which the 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 ϕ 2 and λϕ 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.
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A 2010 study studied this question.