  The physics during the inflationary stage of the universe is of quantum
nature involving extremely high energy densities. Moreover, it is out of
equilibrium on a fastly expanding dynamical geometry. We complement here the
1999 Chalonge Lectures on out of equilibrium fields in self-consistent
inflationary dynamics [astro-ph/0006446] investigating inflation driven by the
evolution of highly excited quantum states. These states are characterized by a
non-perturbatively large number of quanta in a band of momenta and with zero or
nonzero expectation value of the inflaton scalar field. They represent the
situation in which initially a non-perturbatively large energy density is
localized in a band of high energy quantum modes and are coined tsunami-waves.
The self- consistent evolution of this quantum state and the scale factor is
studied analytically and numerically. It is shown that the time evolution of
these quantum states lead to two consecutive stages of inflation under
conditions that are the quantum analogue of slow-roll. The evolution of the
scale factor during the first stage has new features that are characteristic of
the quantum state. During this initial stage the quantum fluctuations in the
highly excited band build up an effective homogeneous condensate with a
non-perturbatively large amplitude as a consequence of the large number of
quanta.The second stage of inflation is similar to the usual classical chaotic
scenario but driven by this effective condensate.The excited quantum modes are
superhorizon in the first stage and do not affect the power spectrum of scalar
perturbations.Thus, this tsunami quantum state provides a field theoretical
justification for chaotic scenarios driven by a classical homogeneous scalar
field of large amplitude.
