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 } eV to 7.25 \times 10 ^ { -33 } 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 8.10 h ^ { -1 } Gyr to 12.2 h ^ { -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 live at a special time in the evolution of the universe . PACS numbers : 98.80.Cq , 04.62.+v , 98.80.Es WISC-MILW-99-TH-10