  The physics of the inflationary universe requires the study of the out of
equilibrium evolution of quantum fields in curved spacetime. We present the
evolution for both the geometry and the matter (described by the quantum
inflaton field) by means of the non-perturbative large N limit combined with
semi-classical gravitational dynamics including the back-reaction of quantum
fluctuations self-consistently for a new inflation scenario. We provide a
criterion for the validity of the classical approximation and a full analysis
of the case in which spinodal quantum fluctuations drive the evolution of the
scale factor. Under carefully determined conditions, we show that the full
field equations may be well approximated by those of a single composite field
which obeys the classical equation of motion in all cases. The de Sitter stage
is found to be followed by a matter dominated phase. We compute the spectrum of
scalar density perturbations and argue that the spinodal instabilities are
responsible for a `red' spectrum with more power at longer wavelengths. A
criterion for the validity of these models is provided and contact with the
reconstruction program is established.
