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 dif ferent cosmological N-body simulations. The data have 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 d imensions also allows the correct use of the appropriate angular diameter d istances. Our results are presented on the basis of the filled-beam approximation in view of the variable particle softening scheme in our algorithm. The import ance of the smoothness of matter in the Universe for the weak lensing resul ts 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 cosmol ogy has implications for the determination of the cosmological parameters f rom high-redshift type Ia supernovae, The possibility of determining the de nsity parameter from the non-Gaussianity in the probability distribution fo r the convergence is discussed.