Preheating in Hybrid Inflation

We investigate a possibility of preheating in hybrid inflation. This scenario involves at least two scalar fields, the inflaton field $\phi$, and the symmetry breaking field $\sigma$. We found that the behavior of these fields after inflation, as well as the possibility of preheating, depends crucially on the ratio of the coupling constant $\lambda$ (self-interaction of the field For $\lambda \gg g^2$, oscillations of the field $\sigma$ soon after inflation become very small, and all energy is concentrated in the oscillating field light scalar (or vector) fields~$\chi$. For $\lambda \sim g^2$ both fields motion stabilizes, and parametric resonance with production of $\chi$ particles becomes possible. For $\lambda \ll g^2$ parametric resonance typically does not occur, though some exceptions from this rule are possible. 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.