Evolution of Inflationary Universe in Extended Gravitational Theories

暴胀宇宙模型是由A.古斯和现在的研究人员独立地，是早期宇宙的标准场景。这不仅被认为是基本相互作用统一理论的结果，而且是宇宙创造的重要步骤。这个模型也得到了观察的支持。最近COBE（Cosmic background explorer）发现了背景辐射的涨落，并发现涨落的谱与暴胀模型的预言非常一致，尽管暴胀模型取得了成功，但非均匀各向异性宇宙能否演化为均匀各向同性宇宙仍是一个严峻的问题。本研究利用广义相对论计算的新形式--Regge演算，对“宇宙无毛猜想”进行了研究。对于均匀各向异性的宇宙，不仅对一般的指数膨胀宇宙模型，而且对幂律膨胀宇宙模型，都找到了演化到暴胀宇宙的初始条件的约束。我们还研究了早期宇宙在相变过程中拓扑缺陷的形成，发现在大爆炸模型中，“织构”为结构的形成提供了一致的密度涨落，特别是对高斯的偏离有助于大尺度结构的形成。

Inflationary Universe model, which was proposed by A. Guth and present researcher independently, is a standard scenario of early universe. This is recognized not only as a consequence of unified theories of elementary interaction, but as an essential step of the creation of universe. This model is also supported by observations. Recently COBE (Cosmic background explorer) discovered the fluctuation of background radiation, and found that the spectrum of the fluctuations is very consistent with the prediction of Inflationary model.In spite of the success of this model, there is a severe problem whether any inhomogeneous and anisotropic universe can evolve to homogeneous and isotropic universe or not. In this research, we investigated this problem called "Cosmic No-hair Conjecture" by using new formalism of the calculation of general relativity, Regge Calculus. For the homogeneous and anisotropic universe, we found the constraint for the initial condition which evolve to inflationary universe not only for usual exponential expanding universe model, but also for the power law expanding models. However, there still remains problem that Hamiltonian constraint is inconsistent with evolution equations for inhomogeneous models.We also investigated formation of topological defects in early universe during phase transition, and showed that "texture" give a consistent density fluctuation for structure formation in the Big Bang Model,in particular, the deviation from Gaussian helps the formation of large scale structure.