  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
{\it 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 < sigma_* < 200
km/s (68% CL), and 158 km/s < sigma_* < 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 < beta < 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.
