臺灣博碩士論文加值系統

大霹靂理論無疑是近代物理學中最迷人和最重要的理論之一。然而，在大霹靂理論中常被提及的空間膨脹，卻也是最易被誤解的物理概念之一。本文透過對宇宙學上三種視界—粒子視界、事件視界和哈伯半徑－之探討，試圖釐清各種不同的膨脹宇宙模型的樣貌。我們同時也討論常令人困惑的宇宙紅移與距離和速度的關係。最後，根據Harrison在1995年所提出「繫鏈星系」這個假想實驗的機制來鑽研宇宙膨脹的本質，以及空間膨脹在各種不同宇宙模型所造成的影響。

The big-bang theory is arguably one of the most fascinating and significant theories in modern physics. However, an expanding space－the major notion of the big-bang cosmology－is also one of the most confusing concepts in modern physics. In this thesis, we first explore various models of expanding universe by virtue of three cosmological horizons, i.e. the particle horizon, the event horizon, and the Hubble radius. We then discuss some of the most perplexing features of the big-bang cosmology, such as cosmological redshifts and the receding velocity of distant galaxies. Finally, based on the gedanken experiment of the “tethered galaxy” proposed by Harrison in 1995, we investigate the very nature of space expansion and its consequences in different cosmological models.

摘要 1
Abstract 2
致謝辭 3
第一章、導論 6
1.1宇宙學背景知識 6
1.2宇宙紅移 10
1.3都卜勒紅移 11
1.31都卜勒紅移和宇宙紅移的比較 12
第二章、宇宙的視界 14
2.1宇宙視界的介紹 14
2.11粒子視界 14
2.12事件視界 15
2.13哈伯半徑 17
2.2一般人對宇宙膨脹的誤解 19
2.21可見宇宙的大小 19
2.22星系會遠離的比光速還快？違反狹義相對論？ 20
2.23可見到後退速度比光快的星系？ 21
2.3ΛCDM基準模型的宇宙視界 22
2.4 不同宇宙模型宇宙視界的比較 25
第三章、宇宙膨脹 29
3.1宇宙膨脹本質的討論 29
3.2用「繫鏈星系」探討宇宙膨脹的效應 30
3.3膨脹的宇宙模型，膨脹使繫鏈星系最終加入哈伯流 32
3.31以紅移表示共動距離和物理距離 34
3.4膨脹的加速決定繫鏈星系接近或遠離 35
3.41以尺度因子表示減速參數和物理距離 36
3.5以紅移討論重新收縮的宇宙模型 37
3.6繫鏈星系的紅移 39
第四章、結論 41
附錄一、狹義相對論的都卜勒公式 42
附錄二、不同組成的宇宙模型 42
(A)宇宙由物質和宇宙常數組成 42
(B)宇宙由物質組成 43
(C)宇宙由宇宙常數組成 43
(D)宇宙由物質和曲率組成 44
附錄三、各種模型哈伯半徑的演化 44
參考資料 46

main reference
[1] Tamara M. Davis Charles H. Lineweaver, “Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe”, arXiv:astro-ph/0310808 v2 13 Nov 2003
[2]Tamara M. Davis, Charles H. Lineweaver, and John K. Webb, “Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects” ,American Journal of Physics 71, 358 (2003)
[3] Matthew J. Francis1,4, Luke A. Barnes1,2, J. Berian James1,3& Geraint F. Lewis1, “Expanding Space: the Root of all Evil?” ,Publications of the Astronomical Society of Australia 24, 95–102 (2007)
[4] Edward R. Harrison, ”The science of the universe , Cosmology” , second edition ,p439~p.441,p.451
[5] David W. Hogg, ”Distance measures in cosmology”, arXiv:astro-ph/9905116 v4 16 Dec 2000
[6] J. E. Felten and R. Isaacman, “Scale factors R(t) and critical values of the cosmological constant Λ in Friedmann universes,” Rev. Mod. Phys. 58, 689–698 (1986).
[7]Edward R. Harission, “Mining energy in an expanding universe.” ,The Astrophysical Journal, 1995
[8]Malcolm S. Longair, “Galaxy formation”,ISBN：978-3-540-51315-5
[9]Stephen Hawking, “The Universe in a Nutshell”,P.31-40, ISBN 0-553-80202
[10]T ony Hey, Anthony J. G. Hey, Patrick Walters, “Einstein’s Mirror”
[11] Stephen Lee “A look at tethered and untethered galaxies”, astro-ph/0104349
[12] Barnes L., Francis M. J., James, J. B. Lewis G. F. 2006, MNRAS, 373, 382