  We show that the vacuum energy of a free quantized field of very low mass can
significantly alter the recent expansion of the universe. The effective action
of the theory is obtained from a non-perturbative sum of scalar curvature terms
in the propagator. We numerically investigate the semiclassical Einstein
equations derived from it. As a result of non-perturbative quantum effects, the
scalar curvature of the matter-dominated universe stops decreasing and
approaches a constant value. The universe in our model evolves from an open
matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble
constant during the present de Sitter epoch, as well as the time at which the
transition occurs from matter-dominated to de Sitter expansion, are determined
by the mass of the field and by the present matter density. The model provides
a theoretical explanation of the observed recent acceleration of the universe,
and gives a good fit to data from high-redshift Type Ia supernovae, with a mass
of about 10^{-33} eV, and a current ratio of matter density to critical
density, Omega_0 <0.4 . The age of the universe then follows with no further
free parameters in the theory, and turns out to be greater than 13 Gyr. The
model is spatially open and consistent with the possibility of inflation in the
very early universe. Furthermore, our model arises from the standard
renormalizable theory of a free quantum field in curved spacetime, and does not
require a cosmological constant or the associated fine-tuning.
