Implications of the lens redshift distribution of strong lensing systems: cosmological parameters and the global properties of early-type galaxies

Abstract

In this paper, we assemble a well-defined sample of early-type gravitational lenses extracted from a large collection of 158 systems, and use the redshift distribution of galactic-scale lenses to test the standard cosmological model ($Λ$CDM) and the modified gravity theory (DGP). Two additional sub-samples are also included to account for possible selection effect introduced by the detectability of lens galaxies. Our results show that independent measurement of the matter density parameter ($Ω_m$) could be expected from such strong lensing statistics. Based on future measurements of strong lensing systems from the forthcoming LSST survey, one can expect $Ω_m$ to be estimated at the precision of $ΔΩ_m\sim 0.006$, which provides a better constraint on $Ω_m$ than \textit{Planck} 2015 results. Moreover, use the lens redshift test is also used to constrain the characteristic velocity dispersion of the lensing galaxies, which is well consistent with that derived from the optical spectroscopic observations. A parameter $f_E$ is adopted to quantify the relation between the lensing-based velocity dispersion and the corresponding stellar value. Finally, the accumulation of detectable galactic lenses from future LSST survey would lead to more stringent fits of $Δf_E\sim10^{-3}$, which encourages us to test the global properties of early-type galaxies at much higher accuracy.