Classical Preheating and Decoherence
  We establish the equivalence between the quantum evolution of spatially homogeneous oscillations of a scalar field and that of an analogous classical system with certain random initial condition. We argue that this observation can be used for numerical simulation of the Universe in the preheating epoch. We also explicitly demonstrate that the phenomenon of parametric resonance that leads to preheating is simultaneously an effective mechanism for generating quantum decoherence of the Universe. 
D.T.Son