TOWARDS THE THEORY OF REHEATING AFTER INFLATION

Reheating after inflation occurs due to particle production by the osc illating inflaton field. In this paper we briefly describe the perturb ative approach to reheating, and then concentrate on effects beyond th e perturbation theory. They are related to the stage of parametric res onance, which we call preheating. It may occur in an expanding univers e if the initial amplitude,of oscillations of the inflaton field is la rge enough. We investigate a simple model of a massive inflaton field phi coupled to another scalar field chi with the interaction term g(2) phi(2) chi(2). Parametric resonance in this model is very broad. It o ccurs in a very unusual stochastic manner, which is quite different fr om parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflato n field experience a series of kicks which, because of the rapid expan sion of the universe, occur with phases uncorrelated to each other. De spite the stochastic nature of the process, it leads to exponential gr owth of fluctuations of the field chi. We call this process stochastic resonance. We develop the theory of preheating taking into account th e expansion of the universe and back reaction of produced particles, i ncluding the effects of rescattering. This investigation extends our p revious study of reheating after inflation. We show that the contribut ion of the produced particles to the effective potential V(phi) is pro portional not to phi(2), as is usually the case, but to \phi\. The pro cess of preheating can be divided into several distinct stages. In the first stage the back reaction of created particles is not important. In the second stage back reaction increases the frequency of oscillati ons of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of chi particles on the oscillating inflaton field terminate the resonance. We calculat e the number density of particles n(chi) produced during preheating an d their quantum fluctuations [chi(2)] with all back reaction effects t aken into account. This allows us to find the range of masses and coup ling constants for which one can have efficient preheating. In particu lar, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.