Abstract
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 $\ensuremath{\Lambda}$ (``quintessence'') models: pseudo Nambu-Goldstone bosons $[V(\ensuremath{\varphi}{)=M}^{4}(1+\mathrm{cos}(\ensuremath{\varphi}/f))]$ and an inverse power-law potential $[V(\ensuremath{\varphi}{)=M}^{4+\ensuremath{\alpha}}{\ensuremath{\varphi}}^{\ensuremath{-}\ensuremath{\alpha}}].$ We show that a large region of parameter space is consistent with current data if ${\ensuremath{\Omega}}_{m0}>0.15.$ On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, ${\ensuremath{\Omega}}_{m0}>0.3,$ considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant.
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