Assessing the effect of lens mass model in cosmological application with
  updated galaxy-scale strong gravitational lensing sample
  By comparing the dynamical and lensing masses of early-type lens galaxies,
one can constrain both the cosmological parameters and the density profiles of
galaxies. We explore the constraining power on cosmological parameters and the
effect of the lens mass model in this method with 161 galaxy-scale strong
lensing systems, which is currently the largest sample with both high
resolution imaging and stellar dynamical data. We assume a power-law mass model
for the lenses, and consider three different parameterizations for $\gamma$
(i.e., the slope of the total mass density profile) to include the effect of
the dependence of $\gamma$ on redshift and surface mass density. When treating
$\delta$ (i.e., the slope of the luminosity density profile) as a universal
parameter for all lens galaxies, we find the limits on the cosmological
parameter $\Omega_m$ are quite weak and biased, and also heavily dependent on
the lens mass model in the scenarios of parameterizing $\gamma$ with three
different forms. When treating $\delta$ as an observable for each lens, the
unbiased estimate of $\Omega_m$ can be obtained only in the scenario of
including the dependence of $\gamma$ on both the redshift and the surface mass
density, that is $\Omega_m = 0.381^{+0.185}_{-0.154}$ at 68\% confidence level
in the framework of a flat $\Lambda$CDM model. We conclude that the significant
dependencies of $\gamma$ on both the redshift and the surface mass density, as
well as the intrinsic scatter of $\delta$ among the lenses, need to be properly
taken into account in this method.
