由Quintessencec和Phantom組成雙純量場的暗能量模型

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吳兆穎(Jhao-Ying Wu) 查詢紙本館藏

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物理學系

論文名稱

由Quintessencec和Phantom組成雙純量場的暗能量模型
(Two-field Models for Dark Energy with Quintessence and Phantom)

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摘要(中)

宇宙的加速膨脹暗示暗能量的存在，暗能量即意謂狀態函數小於負1/3。其中狀態函數定義為壓力與能量密度的比值。舊的暗能量模型像是Quintessence和Phantom,它們只能個別表述狀態函數大於負1和小於負1的分佈。根據最近天文研究觀測，我們宇宙現在的狀態函數是有可能落於小於負1的。因此若要適當地描述宇宙從大爆炸到如今的演化過程，我們就需要另一個能跨越狀態函數等於負1的暗能量模型。
第一個能跨越此一宇宙界線的模型是Quintom，它是結合Quintessence和Phantom 兩個模型而來。第2個模型是Hessence，它是經由一連串的數學轉換，將Quintom模型中原本互相獨立的兩個純量場偶合成單一純量場和一內部對稱的結構。從第2章到第4章有各模型詳細的分析討論，包括改變它們的初始值以得到不同的狀態函數分佈。第5章則是結論及討論。

論文目次

1 Introduction 1
2 Quintessence and Phantom 5
2.1 Quintessence with Exponential Potential . . . . . . . . . . . . . . . . . . . . . . . .9
2.1.1 Exact solution (Particular case) . . . . . . . . . . . . . . . . . . . . . . . . .9
2.1.2 Rolling down model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.1.3 Rolling up model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Phantom with Exponential Potential . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.2.1 Exact solution (Particular case) . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.2.2 Rolling up model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
2.2.3 Rolling down model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Quintom 17
3.1 Quintom with Exponential Potential . . . . . . . . . . . . . . . . . . . . . . . . . . ..18
3.1.1 Quintessence rolling down and phantom rolling up model . . . . ..18
3.1.2 Quintessence rolling down and phantom rolling down model . . .20
3.1.3 Quintessence rolling up and phantom rolling up model . . . . . . . .20
3.1.4 Quintessence rolling up and phantom rolling down model . . . . . 24
4 Hessence 27
4.1 Hessence with Exponential Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 Rolling down model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.2 Rolling up model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
5 Conclusion 37
Bibliography 39
A Mathematica Programs 43

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指導教授

陳江梅(Chiang-Mei Chen)

審核日期

2005-6-27

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