We use the statistics of strong gravitational lensing from the CLASS survey to impose constraints on the velocity dispersion and density profile of elliptical galaxies .
This approach differs from much recent work , where the luminosity function , velocity dispersion and density profile were typically assumed in order to constrain cosmological parameters .
It is indeed remarkable that observational cosmology has reached the point where we can consider using cosmology to constrain astrophysics , rather than vice versa .
We use two different observables to obtain our constraints ( total optical depth and angular distributions of lensing events ) .
In spite of the relatively poor statistics and the uncertain identification of lenses in the survey , we obtain interesting constraints on the velocity dispersion and density profiles of elliptical galaxies .
For example , assuming the SIS density profile and marginalizing over other relevant parameters , we find 168 { km / s } \leq \sigma _ { * } \leq 200 { km / s } ( 68 % CL ) , and 158 { km / s } \leq \sigma _ { * } \leq 220 { km / s } ( 95 % CL ) .
Furthermore , if we instead assume a generalized NFW density profile and marginalize over other parameters , the slope of the profile is constrained to be 1.50 \leq \beta \leq 2.00 ( 95 % CL ) .
We also constrain the concentration parameter as a function of the density profile slope in these models .
These results are essentially independent of the exact knowledge of cosmology .
We briefly discuss the possible impact on these constraints of allowing the galaxy luminosity function to evolve with redshift , and also possible useful future directions for exploration .