Creation and Evolution of Nonlinear Inhomogeneous Spacetime Structures and Numerical Cosmology

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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