Lens Model Degeneracy and Cosmological Tests by Strong Gravitational Lensing

We study the relation between the gravitational lensing observables and the lens model and the cosmological parameters. We estimate the sensitivity of the lensing observables to the lens model and to the cosmological parameters. We show that the observables are primarily dependent on the lens model, while the dependence on cosmological parameters is minor (especially so for the dark energy parameters). We demonstrate the lens model degeneracy by showing both the projected mass density profile and the circular velocity profile. The degeneracy of the projected mass model may not be broken even when combined with the measurements of the velocity dispersion. We also suggest the possible source of the problem of fitting the averaged mass profile of CL 0024+1654 by the Navarro-Frenk-White profile.