  In this work we investigate the behavior of two-dimensional (2D) cosmological
models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A
geometrical term, non-linear in the scalar curvature $R$, is added to the JT
dynamics to test if it could play the role of dark energy in a 2D expanding
universe. This formulation makes possible, first, the description of an early
(inflationary) 2D universe, when the van der Waals (vdW) equation of state is
used to construct the energy-momentum tensor of the gravitational sources.
Second, it is found that for later times the non-linear term in $R$ can
generate an old 2D universe in accelerated expansion, where an ordinary matter
dominated era evolves into a decelerated/accelerated transition, giving to the
dark energy effects a geometrical origin. The results emerge through numerical
analysis, following the evolution in time of the scale factor, its
acceleration, and the energy densities of constituents.
