  In a new model that we proposed, nonperturbative vacuum contributions to the
effective action of a free quantized massive scalar field lead to a
cosmological solution in which the scalar curvature becomes constant after a
time $t_j$ (when the redshift $z \sim 1$) that depends on the mass of the
scalar field and its curvature coupling. This spatially-flat solution implies
an accelerating universe at the present time and gives a good one-parameter fit
to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and
energy density of the universe. Here we show that the imaginary part of the
nonperturbative curvature term that causes the cosmological acceleration,
implies a particle production rate that agrees with predictions of other
methods and extends them to non-zero mass fields. The particle production rate
is very small after the transition and is not expected to alter the nature of
the cosmological solution. We also show that the equation of state of our model
undergoes a transition at $t_j$ from an equation of state dominated by
non-relativistic pressureless matter (without a cosmological constant) to an
effective equation of state of mixed radiation and cosmological constant, and
we derive the equation of state of the vacuum. Finally, we explain why
nonperturbative vacuum effects of this ultralow-mass particle do not
significantly change standard early universe cosmology.
