The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe .
By comparing predicted strong lensing probabilities with observations , we can test the mass distribution of dark matter halos , in particular , the inner density slope .
In this letter , unlike previous work that directly models the density profiles of dark matter halos semi-analytically , we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White ( GNFW ) models of three populations with slopes , \alpha , of about -1.5 , -1.3 and -1.1 for galaxies , groups and clusters , respectively .
This approach is an alternative and independent way to examine the slopes of mass density profiles of halos .
We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant \Lambda .
It is shown that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data .
Together with the previous work on lensing probability , our results suggest that a singular isothermal sphere mass model of less than about 10 ^ { 13 } h ^ { -1 } M _ { \sun } can predict strong lensing probabilities that are consistent with observations of small splitting angles .