New constraints from high redshift supernovae and lensing statistics upon scalar field cosmologies

We explore the implications of gravitationally lensed quasistellar objects 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 $\left[V\right(\phi {)=M}^4(1+\cos (\phi /f\left)\right)]$ and an inverse power-law potential $\left[V\right(\phi {)=M}^{4+\alpha }{\phi }^{-\alpha }].$ We show that a large region of parameter space is consistent with current data if ${\Omega }_{m0\mathrm{}}>\mathrm{0.15.}\mathrm{}$ On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, ${\Omega }_{m0\mathrm{}}>0.3,$ considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant.