Determing the Dark Matten Distribution and The Cosmological Pavameters by Gavitational Lensing

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We develop an approximation scheme to construct the spacetime representing a realistic inhomogeneous universe within the framework of general relativity. The scheme allows us to treat the situation where the spacetime has locally nonlinear density contrast, but is homogeneous and isotropic in a global scale. Thus the constructed spacetime should be used for the analysis of the light propagation in our universe which is the theoretical foundation of the observational cosmology. For the application of the present approximation, we shall investigate the propagation of light ray and propose a simple new derivation of the gravitational lens equation which is free from ad hoc assumptions in the conventional treatment and is totally consistent in the framework of general relativity. the validity of the conventional lens equation.