  In this work we analyze the effects produced by bosonic and fermionic
constituents, including quantum corrections, in two-dimensional (2D)
cosmological models. We focus on a gravitational theory related to the
Callan-Giddings-Harvey-Strominger model, to simulate the dynamics of a young,
spatially-lineal, universe. The cosmic substratum is formed by an {\it
inflaton} field plus a matter component, sources of the 2D gravitational field;
the degrees of freedom also include the presence of a dilaton field. We show
that this combination permits, among other scenarios, the simulation of a
period of inflation, that would be followed by a (bosonic/fermionic) matter
dominated era. We also analyse how quantum effects contribute to the destiny of
the expansion, given the fact that in 2D we have a consistent (renormalizable)
quantum theory of gravity. The dynamical behavior of the system follows from
the solution of the gravitational field equations, the (Klein-Gordon and Dirac)
equations for the sources and the dilaton field equation. Consistent
(accelerated) regimes are present among the solutions of the 2D equations; the
results depend strongly on the initial conditions used for the dilaton field.
In the particular case where fermions are included as matter fields a
transition to a decelerated expansion is possible, something that does not
happen in the exclusively bosonic case.
