The Cosmic Lens All-Sky Survey: statistical strong lensing, cosmological parameters, and global properties of galaxy populations

Extensive analyses of statistical strong gravitational lensing are performed based on the final Cosmic Lens All Sky Survey (CLASS) well-defined statistical sample of flat spectrum radio sources and current estimates of galaxy luminosity functions per morphological type. The analyses are done under the assumption that galactic lenses are well-approximated by singular isothermal ellipsoids and early-type galaxies evolved passively since redshift $z \sim 1$. Depending on how the late-type galaxy population is treated (i.e., whether its characteristic velocity dispersion is constrained or not), we find for a flat universe with a cosmological constant that the present matter fraction of the present critical density $\Omega_{\rm m} = 0.31^{+0.27}_{-0.14}$ (68%) for the unconstrained case or $0.40^{+0.28}_{-0.16}$ (68%) for the constrained case, with an additional systematic uncertainty of $\approx 0.11$ arising from the present uncertainty in the distribution of CLASS sources in redshift and flux density. For a flat universe with a constant equation of state for dark energy w = $p_x$(pressure)/$\rho_x$(energy density), we find that $w < -0.55^{+0.18}_{-0.11}$ (68%) for the unconstrained case or $w < -0.41^{+0.28}_{-0.16}$ (68%) for the constrained case. For the equal frequencies of oblates and prolates, we find that $\sigma_{*}^{(e)} = 198^{+22}_{-18}$ km s$^{-1}$ (68%) for a `steep' $\alpha^{(e)}=-1$ or $\sigma_{*}^{(e)} = 181^{+18}_{-15}$ km s$^{-1}$ (68%) for a `shallow' $\alpha^{(e)}=-0.54$. Finally, from the relative frequencies of doubly-imaged sources and quadruply-imaged sources, we find that a mean projected mass ellipticity of early-type galaxies $\bar{\epsilon}_{\rm mass} = 0.42$ with a 68% lower limit of 0.28. (Abridged)