Creation and Evolution of Nonlinear Inhomogeneous Spacetime Structures and Numerical Cosmology

在本研究中，我们讨论了宇宙的非均匀性问题，特别是非均匀时空的产生和演化问题。非均匀宇宙是否通过暴胀演化成现在的宇宙是本研究的主要问题之一。为了研究这个问题，我们首先提出了一个数值宇宙学的形式，这是一个自然的引力坍缩的数值相对论的扩展。(1)我们发现了以下两个结果：（1）Goldmartth和皮兰计算的是一维球对称情况，而我们讨论的是带宇宙常数的一维平面对称时空，目的是讨论引力波引起的不均匀性。我们发现所有的时空都演化成德西特空间。这有力地支持了宇宙无毛猜想。(ii)通过模拟和精确解的分析，我们提出了“宇宙箍猜想”，并利用它讨论了一般非人宇宙的暴胀现象 ...更多信息 非均匀时空(2)对于均匀但各向异性的宇宙，我们将Wald定理推广到幂律暴胀的情况，这可以在下面讨论的广义爱因斯坦理论中实现。我们还考虑了广义爱因斯坦理论（Gynecology）中的宇宙学，如Brans-Dicke理论。（1）虽然新的混沌暴胀需要对耦合常数进行微调，但如果考虑Gyndrome中的耦合常数，则这种约束就放松了。我们称之为软通货膨胀。(2)在扩展的膨胀中，有核气泡产生宇宙的不均匀性。通过对气泡膨胀的粗略分析，原始模型似乎被排除在观测之外。然而，我们通过详细分析发现，气泡是在Hawking-Moss模式而不是Coleman-De Lucia模式下成核的，并且在暴胀的初始阶段，薄壁近似被打破。这可能会改变扩展通货膨胀模型的情景。(3)宇宙结构的形成是宇宙学中最重要的课题之一，但至今还没有人知道什么是真实的机制。使用甘精胰岛素，我们寻找一种新的机制。特别地，我们考虑了具有非最小耦合的理论，该理论预测了哈勃参数的振荡，然后为我们提供了宇宙的缓慢膨胀阶段。因此，我们预期在缓慢膨胀阶段，密度扰动会迅速增长。对于某些参数，我们确实发现了密度扰动的大幅增强。不幸的是，宇宙在过去一定有一个非物质的时代，当时有效引力常数是负的。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