臺灣博碩士論文加值系統

在宇宙早期，有一段加速膨脹的過程，而這種加速膨脹的過程可能是起因於純量場模型或來自高階修正項重力場模型的貢獻。而初始的條件或是時空特性，是否會影響早期宇宙演化成今日，在大尺度下等向和均勻的膨脹模式，是宇宙學探討的重點之一。本論文將探討包含高階修正項的重力場模型在 Bianchi type I 空間中的效應，假設宇宙在早期是非等向膨脹，有系統地尋找膨脹解，並且進一步分析這個膨脹解隨著時間演化是否會維持其故有的非等向性。

Inflation in the early universe is a scenario that could be induced by the scalar field model and/or the high derivative gravity model. Moreover, initial conditions of the space time may affect the evolution of the large-scale isotropic and homogeneous universe we observed today. Therefore, we will focus on the evolution of the Bianchi type I anisotropically inflating universe under the influence of a high derivative pure gravity model. Systematic method in finding the solutions of the equation of motion will be presented in this thesis. We will also try to find out whether these solutions are stable or not.

1. 簡介 1
2. 比安基分類 4
2.1 基靈方程式 4
2.2 空間和運動轉變群 6
2.3 比安基分類 9
2.4 Bianchi Type I 14
3. 二階重力模型的運動方程式 16
3.1 Bianchi Type I 的空間特性 16
3.2 對尺度因子變分而得到的運動方程式 19
3.3 確切的運動方程式 22
3.4 對度規常數變分而得到的運動方程式 25
4. 運動方程式的解 32
4.1 運動方程式的解 32
4.2 空間項運動方程式的解 35
4.3 能量條件 38
5. 微擾 41
5.1 微擾的設置 41
5.2 得到確切的矩陣 44
5.3 微擾的解 49
6. 結果討論 51
附錄
A 53
B 55
C 58
D 64
參考文獻 69

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