Gravitational lens statistics and the density profile of dark halos

We investigate the influence of the inner profile of lens objects on gravitational lens statistics, taking into account the effect of magnification bias and both the evolution and the scatter of halo profiles. We take the dark halos as the lens objects and consider the following three models for the density profile of dark halos : the SIS (singular isothermal sphere) profile, the NFW (Navarro-Frenk-White) profile, and the generalized NFW profile, which has a different slope at smaller radii. The mass function of dark halos is assumed to be given by the Press-Schechter function. We find that magnification bias for the NFW profile is an order of magnitude larger than that for SIS. We estimate the sensitivity of the lensing probability of distant sources to the inner profile of lenses and to the cosmological parameters. It turns out that the lensing probability is strongly dependent on the inner density profile as well as on the cosmological constant. We compare the predictions with the largest observational sample, the Cosmic Lens All-Sky Survey. The absence or presence of large splitting events in larger surveys currently underway, such as the Two Degree Field system survey and the Sloan Digital Sky Survey, could set constraints on the inner density profile of dark halos.