New Constraints from High Redshift Supernovae and Lensing Statistics   upon Scalar Field Cosmologies
  We explore the implications of gravitationally lensed QSOs and high-redshift SNe Ia observations for spatially flat cosmological models in which a classically evolving scalar field currently dominates the energy density of the Universe. We consider two representative scalar field potentials that give rise to effective decaying $\Lambda $ (``quintessence'') models: pseudo-Nambu-Goldstone bosons ($V(\phi)=M^4(1+\cos (\phi /f)) $) and an inverse power-law potential ($V(\phi)=M^{4+\alpha}\phi ^{-\alpha}$). We show that a large region of parameter space is consistent with current data if $\Omega_{m0} > 0.15$. On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, $\Omega_{m0} > 0.3$, considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant. 
Ioav Waga (Rio de Janeiro Federal U.) and Joshua A. Frieman (Fermilab   & Chicago U., Astron. Astrophys. Ctr.)