Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models

Gravitational lensing of distant objects caused by gravitational tidal forces from inhomogeneities in the universe is weak in most cases, but it is noticed that it gives a great deal of information about the universe, especially regarding the distribution of dark matter. The statistical values of optical quantities such as convergence, amplification and shear have been derived by many people using various approaches, which include the linear perturbational treatment in the weak limit and the nonlinear treatment considering small-scale matter distribution. In this review paper we compare the following three main approaches: (a) the approach in the multi-lens-plane theory; (b) the approach due to the direct integration method; and (c) the perturbational approach. In the former two approaches inhomogeneous matter distributions are produced in 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 used for the large-scale matter distribution.