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研究生： 盧文傑
Wen-jie Lu
論文名稱： 絕對平行彭卡瑞宇宙
Teleparallel Poincaré Cosmology
指導教授： 李沃龍
Lee, Wo-Lung
學位類別： 博士
Doctor
系所名稱： 物理學系
Department of Physics
論文出版年： 2014
畢業學年度： 102
語文別： 中文
論文頁數： 92
中文關鍵詞： 彭卡瑞規範重力理論 、撓率 、絕對平行化 、宇宙加速膨脹 、自旋流體
英文關鍵詞： Poincaré gauge theory of gravity, torsion, teleparallelism, accelerating expansion universe, spin fluid
論文種類： 學術論文
相關次數： 點閱：132  下載：22 
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    • 我們限制彭卡瑞規範重力理論中的撓率張量的形式以符合絕對平行
    化的條件來描述重力的動力學效應。在物質自旋可忽略的狀況下，絕
    對平行化的彭卡瑞宇宙會與廣義相對論推導出的弗里德曼宇宙完全等
    價。在此架構下，撓率純量可取代宇宙常數，驅動宇宙的加速膨脹。
    當考慮自旋流體時，真空的自旋亦可做為宇宙加速膨脹的可能源頭。
    此外，我們利用由史瓦希-德西特度規所推導出的二個靜態球對稱近似
    解，來檢驗絕對平行化彭卡瑞規範重力理論的有效性。

    We apply the teleparallelism condition to the Poincaré gauge theory of gravity (PGT) and constrain the form of torsion tensor. The resultant teleparallelized cosmology is completely equivalent to the spinless Friedmann cosmology
    derived from Einstein’s general theory of relativity. It turns out that, in terms of the cosmic expansion, the effect of torsion is equivalent to that of the cosmological constant. We then extend such theory to include the spin of
    matter and explore the possibility of accounting for the current accelerating universe by a spinning dark energy. Finally, we confirm the validity of the teleparallelized PGT scheme in a spherical symmetric setting using two examples
    derived from the Schwarzchild-de Sitter metric.

    誌謝.....................................................iii Acknowledgements..........................................v 摘要.....................................................vii Abstract..................................................ix 1 緒論.....................................................1 2 V4 與T4 空間中的重力理論簡介.................................7 2.1 曲率與撓率............................................7 2.2 V4 空間中的重力理論....................................11 2.2.1 廣義相對論.....................................11 2.2.2 f(R) 理論.....................................16 2.3 T4 空間中的重力理論....................................18 2.3.1 絕對平行重力理論.................................21 2.3.2 f(T) 重力理論..................................27 3 彭卡瑞規範重力理論.........................................31 3.1 理論基礎.............................................31 3.2 場方程式.............................................37 3.3 撓率張量的對稱性與分量.................................43 4 絕對平行化彭卡瑞規範重力理論(TPGT)...........................47 4.1 FRW 度規中的絕對平行化彭卡瑞撓率張量.....................47 4.2 撓率張量所造成的宇宙膨脹效應.............................52 4.3 絕對平行化彭卡瑞宇宙...................................54 4.3.1 平坦宇宙.......................................55 4.3.2 開放宇宙.......................................57 4.3.3 封閉宇宙.......................................58 4.4 含有自旋流體的宇宙.....................................59 5 TPGT 的應用..............................................67 5.1 靜態球狀對稱度規.......................................67 5.2 史瓦西-德西特度規......................................72 5.3 太陽系測試...........................................75 5.3.1 檢驗一.........................................75 5.3.2 檢驗二.........................................78 6 結論....................................................81 A FRW 度規中的曲率張量、里契張量與純量曲率......................85 參考文獻...................................................89

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