Fluctuations of Quantum Fields in a Classical Background and Reheating

Abstract

We consider the particle creation process associated with a quantum field χin a time-dependent, homogeneous and isotropic, classical background. It is shown that the field square χ^2, the energy density and the pressure of the created particles have large fluctuations comparable to their vacuum expectation values. Possible effects of these fluctuations on the reheating process after inflation are discussed. After determining the correlation length of the fluctuations in two different models, corresponding to the decay in the parametric resonance regime and in the perturbation theory, it is found that these fluctuations should be taken into account in the final thermalization process, in the back-reaction effects and when the formation of primordial black holes is considered. In both models, by comparing quantum and thermal fluctuations with each other it is observed that very quick thermalization after the complete inflaton decay is not always possible even when the interaction rates are large. On the other hand, when the back-reaction effects are included during the preheating stage, the coherence of the inflaton oscillations is shown to be lost because of the fluctuations in χ^2. Finally, we note that a large fluctuation in the energy density may cause a black hole to form and we determine the fraction of total energy density that goes into such primordial black holes in the model of preheating we consider.