Theoretical study on relativistic inhomogeneous universe

为了显示非均匀宇宙的各种性质，以下三个主题：(1)由规则排列的黑洞组成的宇宙模型的初始数据的构造及其宇宙体积膨胀；(2)无限长的柱状非均匀结构；(3)具有与宇宙学视界尺度相当的大小的球对称空洞的宇宙模型。对于主题(1)，我证明了黑洞宇宙模型的体积膨胀率是由类似于均匀各向同性宇宙模型的方程决定的。对于主题(2)，我得到了一个非常重要的结果，它可能导致宇宙审查假说的反例。对于课题(3)，我研究了宇宙微波背景辐射的光谱、运动学的Sunyaev-Zel‘dovich效应、红移漂移和各向异性密度涨落的演化。这些结果表明，宇宙的不均匀性对决定什么是暗能量以及它的大小非常重要。

In order to show various natures of inhomogeneous universe, the following three subjects ;(1) construction of initial data of a universe model composed of regularly aligned black holes and its cosmic volume expansion ;(2) cylindrical inhomogeneous structures with infinite length ;(3) cosmological model with a spherically symmetric void of a comparable size with a cosmological horizon scale. For the subject(1), I showed that the volume expansion rate of a black hole universe model is determined by an equation similar to that of the homogeneous and isotropic universe model. For the subject(2), I obtain a very significant result that may lead to a counterexample of the cosmic censorship hypothesis. For the subject(3), I studied the spectrum of the cosmic microwave background radiation, kinematic Sunyaev-Zel' dovich effect, redshift drift and the evolution of anisotropic density fluctuations. These results imply that inhomogeneity of the universe is very important to decide what is the dark energy and how large it is.