NEW METHOD FOR DETERMINING CUMULATIVE GRAVITATIONAL LENSING EFFECTS IN INHOMOGENEOUS UNIVERSES - ART. NO. 063501

We present a new approach to calculating the statistical distributions for magnification, shear, and rotation of images of cosmological sour ces due to gravitational lensing. In this approach one specifies an un derlying Robertson-Walker cosmological model together with relevant in formation on the clumping of matter on scales much smaller than the Hu bble radius. The geodesic deviation equation is then integrated backwa rds in time until the desired redshift is reached, using a Monte Carlo procedure wherein each photon beam in effect ''creates its own univer se'' as it propagates. The approach is somewhat similar to that used i n ''Swiss cheese'' models, but the ''cheese'' has been completely elim inated, the matter distribution in the ''voids'' need not be spherical ly symmetric, the total mass in each void need equal the corresponding Robertson-Walker mass only on average, and we do not impose an ''opaq ue radius'' cutoff. The case where the matter in the universe consists of point masses is studied in detail, and it is shown that the statis tical distributions of the lensing images are essentially independent of both the mass spectrum and the clustering properties of the point m asses, provided that the clustering is spherical. Detailed results for the distribution of the magnification of images are presented for the point mass case, as well as a number of other matter distributions. W e apply our results (i) to argue that the positive correlation recentl y found between quasar luminosity and the number of absorption line sy stems is not likely to be due to lensing, and (ii) to determine the am ount of ''noise'' and possible bias produced by lensing in measurement s of q(0) using distant supernovas. [S0555-2821(98)03516-4].