Inflation as an Attractor in Dynamical System and the Isotropy and Homogeneity of the Universe

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In this research, we investigated the problems on the generality of inflation, by which we can believe the present homogeneity and isotropy of the Universe, and found the following results.1. The main theme in this research is whether the universes which were created anisotropically or inhomogeneously call evolve into the present universe through inflation. As for this problem, we clarified the followings: (1) For the homogeneous but anisotropic universe, we know that any spacetimes except for Bianchi type IX always approach the inflationary solution. For Bianchi type IX spacetime, however, the results depend on the initial conditions of the universe, hence we showed from the quantum cosmological point of view that initial conditions which drive the universe into inflation are quite natural. (2) As for inhomogeneous spacetimes, we adopted two methods: (i) Two analytic approaches for symmetric spacetime: one is the so-called "inverse scattering method", and the other the Israel's thin s … More hell method. In both case, we obtained inhomogeneous solutions with a cylindrical or plane- symmetry in de Sitter background, discussing about the cosmic no-hair conjecture. (ii) Numerical Approach for most general three-dimensional spacetime We first calculated a spherically symmetric case, and then started to study the most general three-dimensional case. We developed a new formalism, which will be convenient to simulate the cosmological model in the context of numerical relativity. We discussed how to choose a time slicing in the universe and also found a general solution for the linearized gravitational waves in de Sitter background, discussing the homogenization mechanism of inhomogeneities of spacetimes.2. The unified theories of the fundamental interactions may predict a modification of the Einstein theory at the high energy scale. A quantum corrections provide higher-derivative terms of the metric tensor and a non-minimal couping to scalar fields. Brans-Dicke type theories may be derived from higher-dimensional theories such as a superstring. We investigated whether inflation is a natural phenomenon even in such a generalized Einstein theory. Applying a conformal transformation of the metric tensor, we find that most theories are equivalent to the Einstein theory. Using this equivalence, we found that inflation is a natural phenomenon in most cases. Less