  A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon
from the string theory) and a matter field (classical particles) is analyzed.
The particles are created at the expense of the gravitational energy through an
irreversible process whereas the scalar field is supposed to interact only with
itself and to be minimally coupled with the gravitational field. The
irreversible processes of particle creation are related to the non-equilibrium
pressure within the framework of the extended (causal or second-order)
thermodynamic theory. The scalar field (inflaton or tachyon) is described by an
exponential potential density added by a parameter which represents its
asymptotic value and can be interpreted as the vacuum energy. This model can
simulate three phases of the acceleration field of the Universe, namely,(a) an
inflationary epoch with a positive acceleration followed by a decrease of the
acceleration field towards zero, (b) a past decelerated period where the
acceleration field decreases to a maximum negative value followed by an
increase towards zero, and (c) a present accelerated epoch. For the energy
densities there exist also three distinct epochs which begin with a scalar
field dominated period followed by a matter field dominated epoch and coming
back to a scalar field dominated phase.

General Relativity and Quantum Cosmology