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研究生: 陳岱煒
論文名稱: 宇宙年齡之探討
指導教授: 林文隆
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2003
畢業學年度: 91
語文別: 中文
論文頁數: 105
中文關鍵詞: 宇宙學佛立德曼模
英文關鍵詞: cosmology, Friedman Model
論文種類: 學術論文
相關次數: 點閱:272下載:17
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  • 本文首先敘述在二十世紀時宇宙學上重大發現,並以佛立德曼模
    型為基礎,討論宇宙在不同k值時,宇宙總密度W與減速度參數q 的特性。同時探討宇宙常數L 不為零時,如何從宇宙動力學方程式中得到可能的宇宙模型。接著說明如何從放射性元素的衰變、球狀星團中恆星的演化和白矮星的冷卻等測量方法得到宇宙年齡的下限,並使用最新的觀測資料來得出目前宇宙年齡的下限。之後介紹目前宇宙加速膨脹的觀測證據與現今宇宙參數的最新數值,並且利用不同宇宙模型來探討宇宙年齡的計算方法,將所得的結果與實際的觀測資料相互做比較。最後則提到兩個實驗-SNAP 與Planck 對未來宇宙學的重要性與影響。

    This thesis starts with the important discoveries of cosmology at 20th century and discusses the universe total density W and decelerating parameter q at different curvature k on the Friedman Model. By using qualitative analysis of the universal dynamic equations, we discuss the possible cosmological models with cosmological constant L . Beside using the three methods, the decay of heavy elements, the evolution of stars in the globular clusters, and the cooling of white dwarf , to get the lower limit age
    of the universe, we also use the latest observational data to get the lower limit of the universe. Then we describe the latest parameters of the universe in the present epoch and the evidences of the accelerating universe. According to the different cosmological models, we adapt the latest parameters to get the age of universe and compare the results with the observational data. Finally, it describes the two important experiments, SNAP and Planck, that will make the cosmology more accurate and precise in the future.

    致謝.....................................................I 中文摘要.................................................II 英文摘要.................................................III 目錄.....................................................IV 第一章前言...............................................1 第二章宇宙標準模型.......................................6 2.1 宇宙學原理...........................................7 2.2 二十世紀宇宙學的重要發現.............................8 2.2.1 哈伯定律...........................................8 2.2.2 宇宙背景輻射.......................................9 2.2.3 宇宙大爆炸製核理論與輕元素含量.....................10 2.2.4 宇宙背景輻射異向性.................................11 2.2.5 加速膨脹的宇宙.....................................12 2.3 佛立德曼模型.........................................13 2.4 0 = L 時,不同k值的宇宙模型特性.....................18 第三章宇宙常數0 ¹ L 時的宇宙模型.........................19 3.1 0 ¹ L 宇宙模型的定性討論.............................19 3.2 不同k值時的宇宙.....................................21 3.3 0 ¹ WL 時臨界宇宙的解................................26 第四章宇宙年齡的測定方法.................................27 4.1 放射性元素測年法.....................................27 4.3 星體演化測年法.......................................31 4.4 白矮星冷卻測年法.....................................34 第五章宇宙加速膨脹的證據與宇宙常數.......................38 5.1 Ia 型超新星的觀測...................................39 5.2 宇宙微波背景異向性與宇宙總密度0 W ...................41 5.3 宇宙物質密度m W 的測量...............................43 5.4 現今的宇宙學參數.....................................46 第六章宇宙年齡的計算.....................................48 6.1 宇宙能量密度的組成...................................48 6.2 宇宙年齡的計算.......................................50 6.3 愛因斯坦-狄西特宇宙年齡的計算.......................53 6.4 有宇宙常數L 存在的平坦宇宙年齡計算...................54 6.5 宇宙在紅移為z時的年齡計算...........................56 6.6 暗能量的存在對宇宙年齡計算的影響.....................57 第七章結論...............................................60 附錄.....................................................63 附錄A 宇宙動力學方程式的推導............................63 附錄B 由宇宙動力學方程式推導出L W 與m W 關係式..........70 附錄C 利用放射性元素的衰變來求得時間....................75 附錄D 場論中r 與p關係式的推導...........................76 參考資料.................................................79 圖形.....................................................84

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