Robust Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, φ(σ), to derive lens statistics constraints on ΩΛ and Ωm. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of φ(σ) and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of ΩΛ = 0.74–0.78 for a spatially flat universe (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of ΩΛ < 0.86. If φ(σ) instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for ΩΛ becomes 0.72–0.78, with the 95% confidence upper bound ΩΛ < 0.89. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe. Subject headings: cosmological parameters — cosmology: observations — cosmology: theory — gravitational lensing