Structure of Resonance in Preheating after Inflation

Patrick Greene; Lev Kofman; Andrei Linde; Alexei Starobinsky

doi:10.1103/PhysRevD.56.6175

paper

Structure of Resonance in Preheating after Inflation

arXiv:hep-ph/9705347 · doi:10.1103/PhysRevD.56.6175

Abstract

We consider preheating in the theory $1/4 λ ϕ^{4} + 1/2 g^{2} ϕ^{2} χ^{2}$ , where the classical oscillating inflaton field $ϕ$ decays into $χ$ -particles and $ϕ$ -particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter $g^{2} / λ$ . We construct the stability/instability chart in this theory for arbitrary $g^{2} / λ$ . We give simple analytic solutions describing the resonance in the limiting cases $g^{2} / λ ≪ 1$ and $g^{2} / λ ≫ 1$ , and in the theory with $g^{2} = 3 λ$ , and with $g^{2} = λ$ . From the point of view of parametric resonance for $χ$ , the theories with $g^{2} = 3 λ$ and with $g^{2} = λ$ have the same structure, respectively, as the theory $1/4 λ ϕ^{4}$ , and the theory $λ / (4 N) (ϕ_{i}^{2})^{2}$ of an N-component scalar field $ϕ_{i}$ in the limit $N \to \infty$ . We show that in some of the conformally invariant theories such as the simplest model $1/4 λ ϕ^{4}$ , the resonance can be terminated by the backreaction of produced particles long before $< χ^{2} >$ or $< ϕ^{2} >$ become of the order $ϕ^{2}$ . We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.

19 pages, revtex, 12 figures

Structure of Resonance in Preheating after Inflation

Abstract

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