H. J. de Vega

LPTHE, Univ Paris VI

`Out of equilibrium QFT in early cosmology'  

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 present a selfconsistent treatment of inflation where the matter is
described by an scalar QFT while the geometry is dynamically
determined by the Einstein-Friedmann equation. We use out of
equilibrium field dynamics and the non-perturbative large N method to
treat the quantum field.  We consider `new inflation'
type initial conditions. We show that spinodal instabilities drive the growth
of non-perturbatively large quantum fluctuations which shut off the
inflationary growth of the scale factor. We find that 
a very specific combination of  these large quantum
fluctuations plus the inflaton zero mode assemble into a new effective field.
This new field behaves classically and it is the object which actually
rolls down. The metric perturbations during inflation are computed
using this effective field and the Bardeen variable for superhorizon modes
during inflation.  We compute the amplitude and index for the spectrum of
scalar density and tensor perturbations and argue that in all models of this
type the spinodal instabilities are responsible for a `red' spectrum of
primordial scalar density perturbations.
Furthermore, we investigate 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.
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.