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

在广义相对论的框架下，我们发展了一种近似方案来构造表示现实的非均匀宇宙的时空。该格式允许我们处理时空具有局部非线性密度对比度，但在全球尺度上是均匀和各向同性的情况。因此，所构造的时空应该被用来分析光在我们宇宙中的传播，这是观测宇宙学的理论基础。对于本近似的应用，我们将研究光线的传播，并提出一种简单的新的引力透镜方程的推导，它不受常规处理中的特殊假设的影响，并且在广义相对论的框架下完全一致。验证了传统透镜方程的正确性。

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.