臺灣博碩士論文加值系統

觀測的證據顯示我們的宇宙正在膨脹，宇宙學家隨即引入帶有膨脹解的宇宙模型。根據無毛定理的猜想：只有均向膨脹的 de sitter宇宙才是穩定的時空，因此所有非均向膨脹解必然都不穩定。在早期宇宙的研究中，宇宙模型須考慮高階修正項，修正後卻可能得到不一樣的非均向膨脹解。本論文將呈現一些已知的 Bianchi type I 膨脹解，並介紹這些非均向膨脹解是不穩定的證明，這樣的結論說明這些模型符合無毛定理預期的結果。

According to the observation evidences, our universe is an expanding de Sitter space. As a result, many different models have been studied as a natural source of the expanding universe. In particular, higher order corrections terms may be important in the evolution of the early universe. In addition, Gibbons and Hawking come up with the No Hair theorem claiming that the de Sitter solution is the only stable expanding solution. Review on the anisotropically expanding solutions in the Bianchi type I space will be presented in this thesis along with the presentation of the proof of the instability of these expanding solutions. Hence , the result agrees with the conjecture of the no-hair theorem.

Chapter 1. 導論 1
1.1宇宙學簡介 1
1.2宇宙模型與爆漲理論宇宙模型與爆漲理論 1
1.3 FRW宇宙模型 2
1.4 Bianchi宇宙模型 4
1.5 Bianchi type I 宇宙模型 5
Chapter 2. 變分與場方程式 9
2.1 Action Principle 9
2.2變分與Friedmann equation 9
2.3 J.D. Barrow’s variables13
Chapter 3. 求解 17
3.1 equations of motion 17
3.2求解19
Chapter 4. 穩定性分析22
Chapter 5. 結論30
附錄 A 32
附錄 B 33
附錄 C 36
References 40

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