Improved Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital SkySurvey (SDSS) data on the local velocity dispersion distribution function ofE/S0 galaxies, $\phi(\sigma)$, to derive lens statistics constraints on$\Omega_\Lambda$ and $\Omega_m$. Previous studies of this kind relied on acombination of the E/S0 galaxy luminosity function and the Faber-Jacksonrelation to characterize the lens galaxy population. However, ignoringdispersion in the Faber-Jackson relation leads to a biased estimate of$\phi(\sigma)$ and therefore biased and overconfident constraints on thecosmological parameters. The measured velocity dispersion function from a largesample of E/S0 galaxies provides a more reliable method for probing cosmologywith strong lens statistics. Our new constraints are in good agreement withrecent results from the redshift-magnitude relation of Type Ia supernovae.Adopting the traditional assumption that the E/S0 velocity function is constantin comoving units, we find a maximum likelihood estimate of $\Omega_\Lambda =0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertaintyin the number of E/S0 lenses in the CLASS sample), and a 95% confidence upperbound of $\Omega_\Lambda<0.86$. If $\phi(\sigma)$ instead evolves in accordwith extended Press-Schechter theory, then the maximum likelihood estimate for$\Omega_\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound$\Omega_\Lambda<0.89$. Even without assuming flatness, lensing providesindependent confirmation of the evidence from Type Ia supernovae for a nonzerodark energy component in the universe.Comment: 35 pages, 15 figures, to be published in Ap