  By using the thermodynamic theory of irreversible processes and Einstein
general relativity, a cosmological model is proposed where the early universe
is considered as a mixture of a scalar field with a matter field. The scalar
field refers to the inflaton while the matter field to the classical particles.
The irreversibility is related to a particle production process at the expense
of the gravitational energy and of the inflaton energy. The particle production
process is represented by a non-equilibrium pressure in the energy-momentum
tensor. The non-equilibrium pressure is proportional to the Hubble parameter
and its proportionality factor is identified with the coefficient of bulk
viscosity. The dynamic equations of the inflaton and the Einstein field
equations determine the time evolution of the cosmic scale factor, the Hubble
parameter, the acceleration and of the energy densities of the inflaton and
matter. Among other results it is shown that in some regimes the acceleration
is positive which simulates an inflation. Moreover, the acceleration decreases
and tends to zero in the instant of time where the energy density of matter
attains its maximum value.
