Chaotic dynamics in preheating after inflation

Abstract

We study chaotic dynamics in preheating after inflation in which an inflaton $\varphi$ is coupled to another scalar field $\chi$ through an interaction $(1/2)g^2{\varphi }^2{\chi }^2$. We first estimate the size of the quasi-homogeneous field $\chi$ at the beginning of reheating for large-field inflaton potentials $V(\varphi )=V_0{\varphi }^n$ by evaluating the amplitude of the $\chi$ fluctuations on scales larger than the Hubble radius at the end of inflation. Parametric excitations of the field $\chi$ during preheating can give rise to chaos between two dynamical scalar fields. For the quartic potential ($n=4$, $V_0=\lambda /4$) chaos actually occurs for $g^2/\lambda <\mathcal{O}(10)$ in a linear regime before which the backreaction of created particles becomes important. This analysis is supported by several different criteria for the existence of chaos. For the quadratic potential ($n=2$) the signature of chaos is not found by the time at which the backreaction begins to work, similar to the case of the quartic potential with $g^2/\lambda \gg 1$.

12 pages, 10 figures, Version to appear in Classical and Quantum Gravity

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