Chaotic dynamics in preheating after inflation
  We study chaotic dynamics in preheating after inflation in which an inflaton $\phi$ is coupled to another scalar field $\chi$ through an interaction $(1/2)g^2\phi^2\chi^2$. We first estimate the size of the quasi-homogeneous field $\chi$ at the beginning of reheating for large-field inflaton potentials $V(\phi)=V_0\phi^n$ 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 $g^2/\lambda <{\cal O}(10)$ 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 $g^2/\lambda \gg 1$. 
Yoshida Jin and Shinji Tsujikawa