Bianchi Type II 宇宙模型之研究

Abstract

這篇論文主要研究,在Einstein-Hilbert以及Induce gravity模型,Bianchi第二型度規下場方程式以及解的行為,我們將用 變分方式得到場方程式,用愛因斯坦方程式來檢驗我們變分的結果是否正確,在此過程中,我們主要討論Bianchi typeII,並 且詳盡地推導每一個步驟,在試著將情況推廣成所有Bianchi模型通式。接下來對場方程式微擾,檢驗哈伯常數$H_i(t)$的 穩定性,且驗證Bianchi模型會從不均向性趨向於均向。在此論文中,我們亦用數值模擬的方式,探討在不同時期,尺度因子 的膨脹情況。另外我們也針對早期宇宙的暴脹情形做了計算,利用純量場的誘發重力理論,探討宇宙在大霹靂後,10^{-44}秒 到10^{-36}秒,模擬尺度因子的暴脹情形。

In this thesis we study one of the Bianchi type spaces, type II, which is a homogeneous and anisotropic space. We follow the procedure to calculate the Chrystoffel symbols and curvature tensors and obtain the field equations with the variational method. We first consider the Einstein-Hilbert model with perfect fluid and the induced gravity model at early universe. . We gain the numerical solution and test that the scale factor indeed expands. And we also check the induced gravity model that will indeed inflate the space within the $10^{-44}$ to $10^{-36}$ seconds that can solve the flatness problem. The anisotropy to isotropy is also checked in these models.