New Constraints from High Redshift Supernovae and Lensing Statistics upon Scalar Field Cosmologies

Abstract

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