Theoretical Foundation for Observational Cosmology

罗伯逊-沃克时空描述了宇宙的整体结构。然而，真实的宇宙在不同的尺度上都具有不均一性。如何在广义相对论的框架下描述这些不均质性一直是一个长期存在的问题。我们的研究通过引入空间平均过程和应用后牛顿近似解决了这个问题。这为构造现实宇宙的度规提供了第一近似方案。利用这个方案，我们研究了光线的传播和距离-红移关系定义中的不确定性，距离-红移关系在观测宇宙学中具有重要的基础作用。我们还从数值上研究了局部不均匀对光线传播的影响。对这些研究表明，文献中通常使用的距离在某些情况下并不总是合适的。我们还研究了引力透镜，并提出了一种确定宇宙常数的新方法。密度参数是确定宇宙整体结构的最重要的参数之一。对于一维密度分布，我们得到了高度非线性区域中星系的密度参数与奇特速度之间的关系。

Global structure of the universe is described by the Robertson-Walker spacetime. However the real universe has inhomogeneities in various scales. It has been a long-standing problem how these inhomogeneities may be described in the framework of general relativity. Our research solves this problem by introducing the spatial averaging process and applying the post-Newtonian approximation. This provides the first approximation scheme for constructing the metric of realistic universe.Using this scheme we investigated the propagation of light rays and uncertainties in the definition of the distance-redshift relation which has the fundamental importance in the observational cosmology. We also investigated numerically how local inhomogeneities affect the propagation of light rays. g to these studies it is shown that the distance usually used in the literature is not always appropriate in certain situations.We also studied gravitational lenses and proposed a new method to determine the cosmological constant.The density parameter is one of the most important parameters to determine the global structure of the universe. We obtained a relation between the density parameter and the peculiar velocity of galaxies in highly nonlinear region for an one-dimensional density distribution.