We present a statistical analysis of the final lens sample from the Sloan Digital Sky Survey Quasar Lens Search ( SQLS ) .
The number distribution of a complete subsample of 19 lensed quasars selected from 50,836 source quasars is compared with theoretical expectations , with particular attention to the selection function .
Assuming that the velocity function of galaxies does not evolve with redshift , the SQLS sample constrains the cosmological constant to \Omega _ { \Lambda } = 0.79 ^ { +0.06 } _ { -0.07 } ( { stat . } ) ^ { +0.06 } _ { -0.06 } ( { syst . } ) for a flat universe .
The dark energy equation of state is found to be consistent with w = -1 when the SQLS is combined with constraints from baryon acoustic oscillation ( BAO ) measurements or results from the Wilkinson Microwave Anisotropy Probe ( WMAP ) .
We also obtain simultaneous constraints on cosmological parameters and redshift evolution of the galaxy velocity function , finding no evidence for redshift evolution at z \lesssim 1 in any combinations of constraints .
For instance , number density evolution quantified as \nu _ { n } \equiv d \ln \phi _ { * } / d \ln ( 1 + z ) and the velocity dispersion evolution \nu _ { \sigma } \equiv d \ln \sigma _ { * } / d \ln ( 1 + z ) are constrained to \nu _ { n } = 1.06 ^ { +1.36 } _ { -1.39 } ( { stat . } ) { } ^ { +0.33 } _ { -0.64 } ( { syst . } ) and \nu _ { \sigma } = -0.05 ^ { +0.19 } _ { -0.16 } ( { stat . } ) { } ^ { +0.03 } _ { -0.03 } ( { syst . } ) respectively when the SQLS result is combined with BAO and WMAP for flat models with a cosmological constant .
We find that a significant amount of dark energy is preferred even after fully marginalizing over the galaxy evolution parameters .
Thus the statistics of lensed quasars robustly confirm the accelerated cosmic expansion .