Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models

Gravitational lensing of distant objects caused by gravitational tidal forcesfrom inhomogeneities in the universe is weak in most cases, but it is noticedthat it gives a great deal of information about the universe, especiallyregarding the distribution of dark matter. The statistical values of opticalquantities such as convergence, amplification and shear have been derived bymany people using various approaches, which include the linear perturbationaltreatment in the weak limit and the nonlinear treatment considering small-scalematter distribution. In this review paper we compare the following three main approaches: (a) theapproach in the multi-lens-plane theory; (b) the approach due to the directintegration method; and (c) the perturbational approach. In the former two approaches inhomogeneous matter distributions are producedin the CDM model using $N$-body simulations (the P$^3$M code and the tree-code,respectively). In (c) the power spectrum corresponding to the CDM model is usedfor the large-scale matter distribution.Comment: 30 pages, 13 figure