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

动力系统中作为吸引子的暴胀以及宇宙的各向同性和均质性

基本信息

批准号：
63540205
负责人：
MAEDA Kei-ichi
金额：
$ 1.15万
依托单位：
Waseda University (1989)The University of Tokyo (1988)
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

项目摘要

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

在这项研究中，我们研究了有关通货膨胀的普遍性的问题，通过这些问题，我们可以相信宇宙的当前同质性和各向同性，并找到了以下结果。1。这项研究的主要主题是，是否通过通货膨胀来形成各向异性或不均匀地称为当今宇宙。至于这个问题，我们阐明了以下内容：（1）对于同质但各向异性的宇宙，我们知道，除Bianchi IX型外，所有空间始终始终接近通货膨胀解决方案。但是，对于Bianchi IX型时空，结果取决于宇宙的初始条件，因此我们从量子宇宙学的角度表明，将宇宙转化为通货膨胀的初始条件是很自然的。（2）至于不均匀的空间，我们采用了两种方法：（i）对称时空的两种分析方法：一个是所谓的“反向散射方法”，另一个是以色列的稀薄S…更多地狱方法。在这两种情况下，我们在保姆背景中获得了具有圆柱或平面对称性的不均匀溶液，讨论了宇宙的无头发猜想。（ii）对于大多数一般三维时空的数值方法，我们首先计算了一个球体对称的情况，然后开始研究最通用的三维情况。我们开发了一种新的格式，在数值相对性的背景下，可以方便地模拟宇宙学模型。我们讨论了如何在宇宙中选择一个时间切片，并在设立背景中找到了线性化的引力波的一般解决方案，讨论了Spacetimes的不均匀性的均质化机制。2。基本相互作用的统一理论可以预测爱因斯坦理论在高能量尺度上的修改。量子校正提供了公制张量和标量场非最小政变的更高衍生术语。 Brans-Dicke类型的理论可以源自更高维理论，例如超弦。我们研究了通货膨胀是否是一种自然现象，即使在如此普遍的爱因斯坦理论中。采用度量张量的共形转换，我们发现大多数理论等同于爱因斯坦理论。使用这种等效性，我们发现通货膨胀在大多数情况下是一种自然现象。较少的