Creation and Evolution of Nonlinear Inhomogeneous Spacetime Structures and Numerical Cosmology

在这项研究中，我们讨论了宇宙的非均匀问题，特别是非均匀时空的产生和演化问题。这项研究的主要议题之一是，非均匀宇宙是否通过膨胀演化成现在的宇宙。为了研究这个问题，我们首先给出了一个数值宇宙学的形式，它是引力坍缩的数值相对论的自然扩展.(1)我们发现了以下两个结果：(I)Goldwirth和Piran计算了一维球对称的情况，而我们讨论了一维平面对称时空的宇宙常数，以讨论引力波引起的不均匀性.我们发现，所有的时空都演化到了德西特空间。这有力地支持了宇宙无毛猜想。(Ii)从我们的模拟和对精确解的分析，我们提出了宇宙环猜想，利用它我们可以讨论一般的非人…的暴涨情景(2)对于均匀而各向异性的宇宙，我们推广了指数膨胀情形下的Wald定理，这可以在下面讨论的广义爱因斯坦理论中实现。我们还在广义爱因斯坦理论(GET)中考虑了宇宙学，例如Brans-Dicke理论。：(1)虽然新的和混乱的通货膨胀需要对耦合常数进行微调，但如果我们考虑GET中的耦合常数，那么这种约束就会放松。我们称这种模型为软膨胀。(2)在扩展膨胀中，成核气泡产生宇宙的不均匀性。通过对泡沫膨胀的粗略分析，原始模型似乎被排除在观察之外。然而，通过详细的分析，我们发现气泡是在Hawking-Moss模式而不是Coleman-de Lucia模式中成核的，并且薄壁近似在膨胀的初始阶段被打破。这可能会改变扩展的膨胀模型的一种情景。(3)宇宙中的结构形成是宇宙学中最重要的主题之一，但还没有人知道真正的机制是什么。使用GET，我们寻找了一种新的机制。特别是，我们考虑了非最小耦合理论，它预言了哈勃参数的振荡，从而为我们提供了宇宙的缓慢膨胀相。因此，我们预计密度扰动在缓慢膨胀阶段会快速增长。对于某些参数，我们确实发现密度微扰有很大的增强。不幸的是，宇宙在过去一定经历了一个非物理时代，当时有效引力常数为负值。较少

In this research, we discussed the problems on inhomogeneity of the Universe, in particular, on creation and evolution of inhomogeneous spacetime.1. The one of main topics in this research is whether the inhomogeneous universes evolve into the present universe through inflation. In order to investigate this subject, we first presented a formalism of numerical cosmology, which is a natural extension of numerical relativity for gravitational collapse.(1) We found the following two results :(i) Goldwirth and Piran calculated 1 dimensional spherically symmetric case, while we discussed 1 dimensional planar symmetric spacetime with cosmological constant in order to discuss inhomogeneity due to gravitational waves. We found that all spacetime evolve into de Sitter space. This strongly supports the cosmic no-hair conjecture.(ii) From our simulation and by an analysis of exact solutions, we proposed "Cosmic Hoop Conjecture" by which we can discuss on an inflationary scenario for general inhomo … More geneous spacetime.(2) For the homogeneous but anisotropic universe, we generalized Wald's theorem for the case of power-law inflation, which may be realized in generalized einstein theories discussed below.2. We also considered cosmology in generalized Einstein theories (GETs) such as Brans-Dicke theory. :(1) Although new and chaotic inflation need a fine-tuning in coupling constants, if we consider those in GETs, then such constraints is loosened. We call this model soft inflation.(2) In extended inflation, nucleated bubbles produce inhomogeneity of the Universe. The original model seems to be excluded from observation by a rough analysis of bubble expansion. However, we found by a detailed analysis that bubbles are nucleated in the Hawking-Moss mode instead of the Coleman-De Lucia mode, and the thin wall approximation is broken in an initial stage of inflation. This may change a scenario of the extended inflation model.(3) The structure formation in the Universe is one of the most important topics in cosmology, but no one knows yet what is a real mechanism. Using GETs, we looked for a new mechanism. In particular, we considered the theory with non-minimal coupling, which predicts an oscillation in Hubble parameter and then provides us a slow expanding phase of the Universe. We, hence, expect a rapid growth of the density perturbations in the slow expansion phase. For some parameters, we really found a large enhancement of the density perturbations. Unfortunately, the Universe must had an unphysical era in the past, when the effective gravitational constant was negative. Less