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Abstract
We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a fully thermalized system with a finite temperature. We identify the non-perturbative processes of parametric resonance and spinodal instability taking place during the reheating stage. In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function. Our methods can be easily adapted to simulate reheating at the end of inflation.
Highlights
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We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes
In particular we study the unstable modes in the region where the vacuum 1PI effective action becomes complex and show that such spinodal modes can have a dramatic effect on the evolution of the one-point function
Summary
The first few terms contributing to Γ2, arising from the action (2.4), are shown in figure 2 (the role of the indices in the couplings is related to renormalization and will be explained ). In this work we shall work in the Hartree approximation, which includes only the first term in the series, given by ΓH2. In this case the self-energy has only a singular or local part: iλ Πsg(x) = − 2 ∆(x, x),.
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