Vacuum effects of an ultralow mass particle account for the recent acceleration of the universe

In recent work, we showed that non-perturbative vacuum effects of a very low mass particle could induce, at a redshift of order 1, a transition from a matter-dominated to an accelerating universe. In that work, we used the simplification of a sudden transition out of the matter-dominated stage and were able to fit the type Ia supernovae (SNe-Ia) data points with a spatially open universe. In the present work, we find a more accurate, smooth spatially-flat analytic solution to the quantum-corrected Einstein equations. This solution gives a good fit to the SNe-Ia data with a particle mass parameter m(k) in the range 6.40 X 10(-33) eV to 7.25 X 10(-33) eV. It follows that the ratio of total matter density (including dark matter) to critical density, Ohm(0), is in the range 0.58 to 0.151 and the age to of the universe is in the range 8.10h(-1) to 12.2h(-1) Gyr, where h is the present value of the Hubble constant, measured as a fraction of the value 100 km/(s Mpc). This spatially-flat model agrees with estimates of the position of the first acoustic peak in the small angular scale fluctuations of the cosmic background radiation and with light-element abundances of standard big-bang nucleosynthesis. Our model has only a single free parameter, m(h), and does not require that we five at a special time in the evolution of the universe. [S0556-2821(99)01024-3].