  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 field $\sigma$. 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 $\lambda \gg
g^2$, the oscillations of the field $\sigma$ soon after inflation become very
small, and all the energy is concentrated in the oscillating field $\phi$. For
$\lambda \sim g^2$ 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 $\lambda \ll g^2$ 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 efficient if the effective masses of the fields $\phi$ and $\sigma$ are
much greater than the Hubble constant, or 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.
