Poincaré Gauge Theory with Coupled Even and Odd Parity Spin-0 Dynamic Connection Modes: Isotropic Bianchi Cosmologies

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姓名

何飛宏(Fei-hung Ho) 查詢紙本館藏

畢業系所

物理學系

論文名稱

Poincaré Gauge Theory with Coupled Even and Odd Parity Spin-0 Dynamic Connection Modes: Isotropic Bianchi Cosmologies
(Poincaré Gauge Theory with Coupled Even and Odd Parity Spin-0 Dynamic Connection Modes: Isotropic Bianchi Cosmologies)

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摘要(中)

本研究旨在理解新的動態的龐加萊規範重力理論 (BHN PG model)。此理論中，在簡單與值得探討的情況下，只針對純旋量(spin-0+)與贋純旋量(spin-0-)中之奇耦合與偶耦合與奇偶耦合加以討論，以尋求可觀測又有趣的物理結果。同時，又是基於相對簡單且有意義值得探討的原因，我們將均勻又各向同性的宇宙模型作為背景加以研究;更確切的說，把比安奇(Bianchi) A類的宇宙模型作為研究背景(現代標準宇宙模型就在此類中)，將可找到對應有效的拉格朗日(Lagrangian)與哈密爾頓(Hamiltonian)動態系統。此宇宙模型的拉格朗日方程可導出一組描述此宇宙的微分方程，此組方程與BHN PG model以標準宇宙模型為背景導出之描述宇宙尺度之方程式一致。以此結果作為基礎，再有變化的、詳細的、深入的研討這組微分方程：取曲率為常數、線性化此組微分方程並找出系統震盪的簡振模式(normal modes)以描述現在的宇宙、數值演化此宇宙模型以說明奇偶耦合常數對現代宇宙的影響。此研究可說明宇宙加速膨脹的現象與動態的旋量產生的看不見的繞率對宇宙的影響。

摘要(英)

We are investigating the dynamics of a new Poincaré gauge theory of gravity model,the BHN PG model which has cross coupling between the spin-0^+ and spin-0^- modes, in a situation which is simple, non-trivial, and yet may give physically interesting results that might be observable. To this end we here consider a very appropriate situation—homogeneous-isotropic cosmologies—which is relatively simple, and yet all the modes have non-trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. The constant curvature case is investigated. The first order equations are linearized and the normal modes are found. These turn out to control the asymptotic late time cosmological normal modes. Numerical evolution confirms the late time asymptotic approximation and shows the expected effects of the cross parity pseudoscalar coupling.

關鍵字(中)

★ 龐加萊規範理論
★ 比安其宇宙模型
★ 宇稱不守恒耦合常數

關鍵字(英)

★ Poincaré Gauge Theory
★ Bianchi Cosmology
★ Parity violating coupling constant

論文目次

1 Introduction 1
1.1 Background and Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Overview of PG Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Good Dynamic Scalar Modes . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Mystery of the Accelerating Expansion of the Universe . . . . . . . . . . 3
1.1.4 Odd Parity Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Poincaré Gauge Theory of Gravity 5
2.1 Poincaré Gauge Theory of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Isotropic Bianchi I and IX PGT with Odd Terms in Cosmology 10
3.1 FLRW Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Bianchi I and IX Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Effective Lagrangian and Hamiltonian Analysis 13
4.1 Effective Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.1 Dynamical Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Effective Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2.1 Hamilton equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Further Analysis 21
5.1 Constant Curvature Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Linearized Equations and Normal Modes . . . . . . . . . . . . . . . . . . . . . 23
5.3 Late Time Asymptotic Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 Numerical Demonstration 28
6.1 Numerical Evolution for Constant Curvature Case . . . . . . . . . . . . . . . . . 28
6.2 Numerical Test for Linearized Model . . . . . . . . . . . . . . . . . . . . . . . . 31
6.3 The Effect of Odd Coupling Parameters . . . . . . . . . . . . . . . . . . . . . . 31
6.4 Typical Full Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.5 Accelerating Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7 Summary, Discussion and Conclusion 41
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.1.1 Where We Came From . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.1.2 On the Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.1.3 Continuing on the Trajectory of the Road . . . . . . . . . . . . . . . . . 42
7.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A Appendix 45
A.1 Comparing Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Bibliography 46

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指導教授

聶斯特(James M. Nester)

審核日期

2011-8-17

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