臺灣博碩士論文加值系統

宇宙學家曾對帶有正宇宙常數項的膨脹宇宙模型其終期行為做了一些驗證：目前已知 Bianchi 空間下的愛因斯坦模型只要滿足特定能量條件，宇宙最後一定會演化成一個均勻、均向的 de Sitter space 時空。 早期宇宙在高能量下應該要做修正；於是有宇宙學家導入了高次曲率項來修正早期宇宙模型，並找到一個不均向宇宙的膨脹解。後續的檢驗發現它依然是不穩定的。我們詳細介紹 Wald 有關宇宙演化定理的証明，隨後假設宇宙演化初期起始於 Bianchi type I 空間，在導入了高次項重力模型後，有系統地找出了 de Sitter 空間解和正確的不均向空間解。 最後我們以微擾的方式證實，這個不均向解的確是不穩定的。

Robert Wald showed that anisotropically expanding universes will evolve to a stable de Sitter space for a large class of Einstein gravity models with a positive cosmological constant under certain energy conditions. A detailed review is presented in this paper. It is also found that a class of Bianchi type I expanding solutions exist in the presence of the higher derivative corrections. We provide a detailed derivation of the field equations, and solve for the expanding solutions in a systematic manner. This class of anisotropically expanding soltuions are shown to be unstable by perturbating the field equations in the presence of the expanding background solution.

摘要 ...................................................i
Abstract ..............................................ii
誌謝 .................................................iii
Contents ..............................................iv

Chapter 1. Introduction ...............................1

Chapter 2. Bianchi type I space
2.1. Metric tensor ................................6
2.2. Christoffel symbol ...........................7
2.3. Components of Riemann tensor .................8
2.4. Components of Ricci tensor ...................9
2.5. Ricci scalar ................................10

Chapter 3. Field equations
3.1. Least action principle ......................11
3.2. Field equations .............................12
3.3. B equation and a_{i} equation in Bianchi type I
space .......................................15
3.4. Solutions of field equations ................19
3.5. Energy conditions ...........................20

Chapter 4. Perturbation
4.1. Perturbation equations and the set ..........23
4.2. First order perturbation equations for BH
metric ......................................27
4.3. Perturbation B+a_{1}+a_{2}+a_{3} (trace)
equation ....................................29
4.4. Solve perturbation equations ................31

Chapter 5. Conclusions ...............................33

附錄 A
A.1. Derive the introduction .....................34
A.2. Field equation ..............................43
A.3. B equation and a_{i} equation ...............45
A.4. B perturbation equation and a_{i} perturbation
equation ....................................48
A.5. Bianchi type I metric .......................53

REFERENCE .............................................55

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