  In this work we discuss the possibility of positive-acceleration regimes, and
their transition to decelerated regimes, in two-dimensional (2D) cosmological
models. We use general relativity and the thermodynamics in a 2D space-time,
where the gas is seen as the sources of the gravitational field. An
early-Universe model is analyzed where the state equation of van der Waals is
used, replacing the usual barotropic equation. We show that this substitution
permits the simulation of a period of inflation, followed by a
negative-acceleration era. The dynamical behavior of the system follows from
the solution of the Jackiw-Teitelboim equations (JT equations) and the
energy-momentum conservation laws. In a second stage we focus the
Callan-Giddings-Harvey-Strominger model (CGHS model); here the transition from
the inflationary period to the decelerated period is also present between the
solutions, although this result depend strongly on the initial conditions used
for the dilaton field. The temporal evolution of the cosmic scale function, its
acceleration, the energy density and the hydrostatic pressure are the physical
quantities obtained in through the analysis.
