Theoretical Foundation for Observational Cosmology

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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.