Cosmological solutions with gravitational particle production and
  non-zero curvature
  In a homogeneous and isotropic universe with non-zero spatial curvature we
consider the effects of gravitational particle production in the dynamics of
the universe. We show that the dynamics of the universe in such a background is
characterized by a single nonlinear differential equation which is
significantly dependent on the rate of particle creation and whose solutions
can be dominated by the curvature effects at early times. For different
particle creation rates we apply the singularity test in order to find the
analytic solutions of the background dynamics. We describe the behavior of the
cosmological solutions for both open and closed universes. We also show how the
effects of curvature can be produced by the presence of a second perfect fluid
with an appropriate equation of state. By combining that results with the
analysis of the critical points we find that our consideration can be related
with the pre-inflationary era. Specifically we find that for negative spatial
curvature small changes of the Milne spacetime leads to a de Sitter universe.
