CONSTRAINING COSMOLOGICAL PARAMETERS WITH IMAGE SEPARATION STATISTICS OF GRAVITATIONALLY LENSED SDSS QUASARS: MEAN IMAGE SEPARATION AND LIKELIHOOD INCORPORATING LENS GALAXY BRIGHTNESS

Abstract

Recent large scale surveys such as Sloan Digital Sky Survey have produced homogeneous samples of multiple-image gravitationally lensed quasars with well-defined selection effects. Statistical analysis on these can yield independent constraints on cosmological parameters. Here we use the image separation statistics of lensed quasars from Sloan Digital Sky Survey Quasar Lens Search (SQLS) to derive constraints on cosmological parameters. Our analysis does not require knowledge of the magnification bias, which can only be estimated from the detailed knowledge on the quasar luminosity function at all redshifts, and includes the consideration for the bias against small image separation quasars due to selection against faint lens galaxy in the follow-up observations for confirmation. We first use the mean image separation of the lensed quasars as a function of redshift to find that cosmological models with extreme curvature are inconsistent with observed lensed quasars. We then apply the maximum likelihood test to the statistical sample of 16 lensed quasars that have both measured redshift and magnitude of lens galaxy. The likelihood incorporates the probability that the observed image separation is realized given the luminosity of the lens galaxy in the same manner as Im et al. (1997). We find that the 95% confidence range for the cosmological constant (i.e., the vacuum energy density) is 0.72 ≤ Ω Λ ≤ 1.0 for a flat universe. We also find that the equation of state parameter can be consistent with ?1 as long as the matter density m . 0.4 (95% confidence range). We conclude that the image separation statistics incorporating the brightness of lens galaxies can provide robust constraints on the cosmological parameters.