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Preprint

19 May 1997

We consider preheating in the theory \(1/4 \lambda \phi^4 + 1/2 g^2\phi^2\chi^2 \), where the classical oscillating inflaton field \(\phi\) decays into \(\chi\)-particles and \(\phi\)-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 \(g^2/\lambda\). We construct the stability/instability chart in this theory for arbitrary \(g^2/\lambda\). We give simple analytic solutions describing the resonance in the limiting cases \(g^2/\lambda\ll 1\) and \(g^2/\lambda \gg 1\), and in the theory with \(g^2=3\lambda\), and with \(g^2 =\lambda\). From the point of view of parametric resonance for \(\chi\), the theories with \(g^2=3\lambda\) and with \(g^2 =\lambda\) have the same structure, respectively, as the theory \(1/4 \lambda \phi^4\), and the theory \(\lambda /(4 N) (\phi^2_i)^2\) of an N-component scalar field \(\phi_i\) in the limit \(N \to \infty\). We show that in some of the conformally invariant theories such as the simplest model \(1/4 \lambda\phi^4\), the resonance can be terminated by the backreaction of produced particles long before \(<\chi^2>\) or \(<\phi^2 >\) become of the order \(\phi^2\). We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.

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Lev Kofman, Alexei Starobinsky, Andrei Linde (1994)

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J. Traschen, Y. Shtanov, R. Brandenberger (1994)

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Lev Kofman, Andrei Linde, Alexei Starobinsky (1995)