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 $m_h$ in the range $6.40\times {10}^{-33}\hspace{0.5em}\mathrm{eV}$ to $7.25\times {10}^{-33}\hspace{0.5em}\mathrm{eV}.$ It follows that the ratio of total matter density (including dark matter) to critical density, ${\Omega }_0,$ is in the range 0.58 to 0.15, and the age $t_0$ of the universe is in the range ${8.10h}^{-1}$ to ${12.2h}^{-1}\hspace{0.5em}\mathrm{Gyr},$ where h is the present value of the Hubble constant, measured as a fraction of the value $100\hspace{0.5em}\mathrm{km}/\left(\mathrm{s}\hspace{0.5em}\mathrm{Mpc}\right).\mathrm{}$ 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 live at a special time in the evolution of the universe.