Gravitational Lensing Statistics and Density Profile of Dark Halo

We investigate the influence of the inner profile of the lens objects on gravitational lensing statistics taking into account of the effect of the magnification bias and both the evolution and the scatter of halo profiles. We take the dark matter halos as the lens objects and consider the following three models for the density profile of the dark matter halo; SIS (singular isothermal sphere), the NFW (Navarro Frenk White) profile, and the generalized NFW profile which has a different slope at smaller radii. The number density of the lens is assumed to be given by the Press-Schechter function. We find that the magnification bias for the NFW profile is order of magnitude larger than that for SIS. We estimate the sensitivity of the lensing probability of the distant source to the inner profile of the lens 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 2dF and SDSS could set constraints on the inner density profile of the dark matter halos. Subject headings: cosmology: gravitational lensing — dark matter:clusters