Lensing effects in an inhomogeneous universe

Recently, Holt & Wald have presented a new method for determining gravitati onal lensing effects on, e.g., supernova luminosity Versus redshift measure ments in inhomogeneous universes. In this paper, their method is generalize d in several ways: First, the matter content is allowed to consist of sever al different types of fluids, possibly with non-vanishing pressure. Second, besides lensing by simple point masses and singular isothermal spheres, th e more realistic halo dark matter distribution proposed by Navarro, Frenk & White (NEW), based on N-body simulation results, is treated. We discuss va rious aspects of the accuracy of the method, such as luminosity corrections , and statistics, for multiple images. We find in agreement with other rece nt work that a large sample of supernovae at large redshift could be used t o extract gross features of the mass distribution of the lensing dark matte r halos, such as the existence of a large number of point-like objects. The results for the isothermal sphere and the NFW model are, however, very sim ilar if normalized to the observed luminosity distribution of galaxies. We give convenient analytical fitting formulas for our computed lensing probab ilites as a function of magnification, for several redshifts.