Weak gravitational lensing in different cosmologies, using an algorithm for shear in three dimensions

We present the results of weak gravitational lensing statistics in four different cosmological $N$-body simulations. The data has been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening facility for the $N$-body particle masses, and enables a physical interpretation for the large-scale structure to be made. Working in three-dimensions also allows the correct use of the appropriate angular diameter distances. Our results are presented on the basis of the filled beam approximation in view of the variable particle softening scheme in our algorithm. The importance of the smoothness of matter in the universe for the weak lensing results is discussed in some detail. The low density cosmology with a cosmological constant appears to give the broadest distributions for all the statistics computed for sources at high redshifts. In particular, the range in magnification values for this cosmology has implications for the determination of the cosmological parameters from high-redshift Type Ia Supernov\ae. The possibility of determining the density parameter from the non-Gaussianity in the probability distribution for the convergence is discussed.