  One of the fundamental problems of modern cosmology is to explain the origin
of all the matter and radiation in the Universe today. The inflationary model
predicts that the oscillations of the scalar field at the end of inflation will
convert the coherent energy density of the inflaton into a large number of
particles, responsible for the present entropy of the Universe. The transition
from the inflationary era to the radiation era was originally called reheating,
and we now understand that it may consist of three different stages:
preheating, in which the homogeneous inflaton field decays coherently into
bosonic waves (scalars and/or vectors) with large occupation numbers;
backreaction and rescattering, in which different energy bands get mixed; and
finally decoherence and thermalization, in which those waves break up into
particles that thermalize and acquire a black body spectrum at a certain
temperature. These three stages are non-perturbative, non-linear and out of
equilibrium, and we are just beginning to understand them. In this talk I will
concentrate on the preheating part, putting emphasis on the differences between
preheating in chaotic and in hybrid inflation.
