Assessing the effect of lens mass model in cosmological application with updated galaxy-scale strong gravitational lensing sample.

By comparing the dynamical mass and lensing mass of early type lens galaxies, one can constrain both the cosmological parameters and the density profiles of galaxies. In this paper, we explore the constraining power of this method on cosmological parameters, using a compiled sample of 157 galaxy-scale strong lensing systems, which is currently the largest sample with both high resolution imaging and stellar dynamical data. These selected lenses are all early-type galaxies with E or S0 morphologies and without significant substructures or close companion galaxies. We assume a power-law mass model for the lenses, and consider three different parameterizations for the slope ($\gamma$ ) of the total mass density profile ($\rho(r)\propto r^{-\gamma}$) to include the effect of the dependence of lens mass model on redshift and surface mass density. By fitting simultaneously the cosmological model and the lens mass model, we find that the cosmological parameters are not very well constrained with current data, and the posterior distribution on $\Omega_m$ is heavily dependent on the choice of parameterization for the lens mass model. By employing the Bayesian information criterion, we find the lens mass model including dependencies on both redshift and surface mass density is favored. We observe the dependencies of $\gamma$ on the redshift and the surface mass density at >3$\sigma$ and >5$\sigma$ levels, respectively. We conclude that unless the significant dependencies of $\gamma$ on both the redshift and the surface mass density are properly taken into account, the strong gravitational lensing systems under consideration cannot served as a kind of promising cosmological probes.