Improved Cosmological Constraints from Gravitational Lens Statistics

Abstract

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky\nSurvey (SDSS) data on the local velocity dispersion distribution function of\nE/S0 galaxies, $\\phi(\\sigma)$, to derive lens statistics constraints on\n$\\Omega_\\Lambda$ and $\\Omega_m$. Previous studies of this kind relied on a\ncombination of the E/S0 galaxy luminosity function and the Faber-Jackson\nrelation to characterize the lens galaxy population. However, ignoring\ndispersion in the Faber-Jackson relation leads to a biased estimate of\n$\\phi(\\sigma)$ and therefore biased and overconfident constraints on the\ncosmological parameters. The measured velocity dispersion function from a large\nsample of E/S0 galaxies provides a more reliable method for probing cosmology\nwith strong lens statistics. Our new constraints are in good agreement with\nrecent results from the redshift-magnitude relation of Type Ia supernovae.\nAdopting the traditional assumption that the E/S0 velocity function is constant\nin comoving units, we find a maximum likelihood estimate of $\\Omega_\\Lambda =\n0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertainty\nin the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper\nbound of $\\Omega_\\Lambda<0.86$. If $\\phi(\\sigma)$ instead evolves in accord\nwith extended Press-Schechter theory, then the maximum likelihood estimate for\n$\\Omega_\\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound\n$\\Omega_\\Lambda<0.89$. Even without assuming flatness, lensing provides\nindependent confirmation of the evidence from Type Ia supernovae for a nonzero\ndark energy component in the universe.\n