臺灣博碩士論文加值系統

從WMAP 的微波背景輻射實驗觀察數據中,可知宇宙在大尺度下是均質均向的時空,但微小區域還是存在些許的不均向,而這些微小的不均勻顯示,宇宙演化起始於不均向膨脹。因此,我們將利用 Bianchi type I 空間的特性,加入不同的宇宙"尺度因子",並且在系統中加入高階修正項求解,隨後將運用動力學系統的方法,分析這個解的穩定性。

Form the observation of the cosmic microwave background radiation done by WMAP, the physical universe is highly homogeneous and isotropic with tiny anisotropic distribution reflecting the initial anisotropy of the expanding universe. The Bianchi type I space will be adopted along with higher order correction terms as the physical models in charge of the evolution of the anisotropic ally expanding universe. Expanding solutions can be solved accordingly. The evolution of these solutions can be treated as a dynamical system that provides detailed stability analysis of these solutions.

摘要 i
ABSTRACT ii
致謝 iii
目錄 iv
圖目錄 v
1. Introduction 1
1.1 Background 1
1.2 Einstein Universe 2
1.3 Special Relativity 2
1.4 General Relativity 3
1.5 FRW metrics 6
1.6 De Sitter universe 8
2. Bianchi geometric type 9
2.1 Mathematics conception 9
2.2 Riemannian manifold 9
2.3共變導數 10
2.4 Lie Derivation 11
2.5 Killing equation 12
2.6在二維的的度規空間計算 13
2.7九種三維運動的類型 15
2.8 Bianchi Type I 度規空間 16
2.9 Bianchi Type I different form 17
2.10 All Bianchi Type度規空間 18
2.11 Theory of stability 19


3. Bianchi Type I research 21
3.1 Gravitational action 21
3.2 Equation of Motion 23
3.3導出Equation of Motion 25
3.4在Bianchi type I空間下運動方程式的解 29
3.5找出DE的eigenvalue 並且討論stability的問題 32
4. Conclusions 36
5. Appendix 37
5.1 Appendix A.高階修正項的Einstein Equation 推導 37
5.2 Appendix B.空間與時間的運動方程式 41
5.3 Appendix C.The other method for finding Bianchi Type I solution 43
5.4 Appendix D.Calculate Eigenvalues 54
6. References 58

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