吳俊輝臺灣大學：物理研究所黃智威Huang, Chih-WeiChih-WeiHuang2007-11-262018-06-282007-11-262018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/54574We tested a statistic trying to find out whether there exists a preferred direction in the Cosmic Microwave Background (CMB) in a flat universe with finite topology. Recent observations of the Cosmic Microwave Background indicate that our universe is nearly flat, if not exactly flat, and is strongly consistent with several cosmological models that have finite topologies. In this thesis, first we use a simulation code by Jiun-Huei Proty Wu (National Taiwan University, Taiwan, ROC) to generate full-sky CMB maps in a flat universe with finite topology. Then we apply the preferred-direction statistic on our simulated CMB maps to seek for the level of `preferred directionality'. Unfortunately we can not conclude the final results until we add the Monte Carlo simulations of our model. But this method is still a general technique and it also has the advantage of being easily calculable for the mega-pixel maps which will soon be available.Acknowledgments 1 Abstract 2 1 Introduction 7 1.1 Background Concepts 7 1.1.1 Geometry vs. Topology 7 1.1.2 Topological Manifolds in a Flat Space 8 1.2 Is Our Universe Infinite? 10 1.2.1 The Philosophical Views 10 1.2.2 Observational Hints 11 1.3 CMB in A Finite Universe 12 1.3.1 Symmetry in the Eigen Set 14 1.3.2 The Program of CMB Simulaton 16 2 The Method and Formalism 17 2.1 A Statistical Method 17 2.2 Motivation 18 2.3 The Preferred-Direction Statistic 18 3 Results and Discussion 24 3.1 Group Blocks 24 3.2 Estimate the Gradient Vector gp 26 3.3 Statistics of Simulated CMB Maps 27 3.4 Discussion 29 3.5 Conclusion 30 Appendix 32 A The Program Source Codes 32 A.1 Group Blocks 32 A.2 Find the Preferred Direction 44 References 47675852 bytesapplication/pdfen-US統計宇宙學拓撲平坦模擬偏好方向微波背景輻射CosmologystatisticCosmic Microwave BackgroundtopologysimulationCMBflatpreferred directionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54574/1/ntu-93-R91222042-1.pdf