Preheating in hybrid inflation

We investigate the possibility of preheating in hybrid inflation. This scenario involves at least two scalar fields: the inflaton field phi, and the symmetry breaking held sigma. We found that the behavior of these fields after inflation, as well as the possibility of preheating (particle production due to parametric resonance), depends crucially on the ratio of the coupling constant lambda (self-interaction of the field sigma) to the coupling constant g(2) (interaction of phi and sigma). For lambda much greater than g(2), the oscillations of the field sigma soon after inflation become very small, and all the energy is concentrated in the oscillating field phi. For lambda similar to g(2) both fields sigma and phi oscillate in a rather chaotic way, but eventually their motion stabilizes, and parametric resonance with production of chi particles becomes possible. For lambda much less than g(2) the oscillations of the field phi soon after inflation become very small, and all the energy is concentrated in the oscillating field sigma. Preheating can be very efficient if the effective masses of the fields phi and sigma are much greater than the Hubble constant at the end of inflation, since those fields can then oscillate many times per e-fold, with a large amplitude. Preheating can also be efficient if these fields are coupled to other light scalar (or vector) fields chi. In the recently proposed hybrid models with a second stage of inflation after the phase transition, both preheating and usual reheating are inefficient. Therefore for a very long time the universe remains in a state with vanishing pressure. As a result, density contrasts generated during the phase transition in these models can grow and collapse to form primordial black holes. Under certain conditions, most of the energy density after inflation will be stored in small black holes, which will later evaporate and reheat the universe.