Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

256 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
where the effective pressure obeys an equation of state
For this pressure approaches Effectively, this component
behaves as a vacuum contribution. For it represents stiff
matter with Acording to (32) the radiation component may
be regarded as emerging from the decay of the initial vacuum. One may
introduce a radiation temperature characterized by a dependence
This temperature starts at for then increases
to a maximum value and finally decreases as
for large values of
6. EQUIVALENT SCALAR FIELD
DYNAMICS
Inflationary cosmology is usually discussed in terms of scalar fields
with suitable potentials. The common picture consists of an initial “slow
roll” phase with a dynamically dominating (approximately constant)
potential term, which generates a de Sitter like exponential expansion,
connected with an “adiabatic supercooling”. During the subsequent “reheating”
which in itself is a highly complicated non–equilibrium period,
the scalar field is assumed to decay into “conventional” matter. The entire
entropy in the presently observable universe is produced during the
reheating phase according to these scenarios. As to the mechanism of
entropy production the “standard” (i.e. based on scalar field dynamics)
inflationary picture essentially differs from the fluid particle production
scenario presented here, since in our approach the entropy is produced
already during the period of accelerated expansion. On the other hand,
as far as the behavior of the scale factor is concerned, there exists a
close correspondence between the role of a negative fluid pressure (due
to the production of particles) and a suitable scalar field potential. What
counts here is the magnitude of the effective negative pressure, independently
of its origin (scalar field potential or particle production). What
one would like to have is an interconnection between both these different
lines of describing the early universe. This would allow us to switch from
the scalar field to the fluid picture and vice versa. To this purpose we
start with the familiar identifications
or,