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 Λ (``quintessence'') models: pseudo Nambu-Goldstone bosons [V(φ)=M⁴(1+cos(φ/f))] and an inverse power-law potential [V(φ)=M^4+αφ^-α]. We show that a large region of parameter space is consistent with current data if Ωₘ₀>0.15. On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, Ωₘ₀>0.3, considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant.