Cosmic Topology and Software Development

宇宙拓扑和软件开发

• 批准号: 0452612
• 负责人: Jeffrey Weeks
• 金额: --
• 依托单位: Weeks Jeffrey R
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-05-01 至 2009-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0452612&HistoricalAwards=false
• 关键词: Cosmic; Topology; Software; Development

In a sufficiently small multiconnected universe one expects unusually weak broad-scale fluctuations in the cosmic microwave background (CMB), and that is exactly what the WMAP satellite has observed, at a confidence level of roughly 1-in-300 to 1-in-500. However, the mystery has deepened with the discovery of anomalies in the CMB. Specifically, the broadest fluctuations (the ell=2 and ell=3 modes) align in the direction of the cosmological dipole. Stranger still, radio and optical astronomers have independently observed unexplained anisotropies pointing in the same direction. While it would be premature to draw conclusions, dark matter is high on the list of candidates. Whatever the ultimate explanation, if the broad-scale CMB fluctuations turn out to be weaker than they seem, this will strengthen the case for a finite universe. The current project continues to develop the mathematics of the eigenmodes of finite universe candidates for better comparison with observations, while simultaneously trying to make sense of the anomalies in the data and to gauge their impact on topological conclusions. The educational half of the project is developing and expanding a suite of geometry and topology software, spanning the gamut from specialized research software (SnapPea) to widely used topology games for middle school students.Speculation on the shape of the universe goes back to ancient times, but serious mathematical study of cosmic topology began in 1854 when Riemann proposed the hypersphere as a cosmological model. Topology blossomed in the late 19th century, leading to a variety of possible 3-dimensional spaces. The astronomer Karl Schwarzschild presented these models to the German Astronomical Society in 1900 as candidates for the topology of space, but given the limited observational data available at the time, he could conclude only that the universe must be much larger than our Milky Way galaxy. Indeed cosmic topology made little headway as an observational science until the 1990's when the COBE and WMAP satellites found hints of a finite universe in the cosmic microwave background radiation. The past decade has been a turbulent one, though, with intense work on hyperbolic models giving way to flat and spherical models to accommodate the 1998 discovery of dark energy. More recently the plot has taken a new twist, with features of the cosmic microwave background -- as well as some optical and radio anomalies -- all aligning in the direction of Virgo. This suggests some new physical effect -- perhaps dark matter -- which has not been previously accounted for. The research component of the present project applies geometrical and topological knowledge to the ongoing efforts to understand the shape and nature of our universe, while the educational component makes these breathtakingly beautiful ideas accessible to middle school, high school and college students (www.geometrygames.org).

在一个足够小的多连接宇宙中，人们预计宇宙微波背景(CMB)会出现异常微弱的大范围波动，这正是WMAP卫星在大约1/300到1/500的置信度下观察到的。然而，随着CMB异常的发现，这个谜团变得更加神秘。具体地说，最宽的涨落(ell=2和ell=3模)与宇宙偶极子的方向一致。更奇怪的是，射电天文学家和光学天文学家独立地观测到了指向同一方向的无法解释的各向异性。虽然现在下结论还为时过早，但暗物质在候选名单中的位置很高。无论最终的解释是什么，如果CMB的大尺度波动最终比看起来的要弱，这将加强有限宇宙的理由。目前的项目继续发展有限宇宙候选者的本征模式的数学，以便更好地与观测进行比较，同时试图理解数据中的异常并衡量它们对拓扑结论的影响。该项目的教育部分是开发和扩展一套几何和拓扑软件，从专门的研究软件(SnapPea)到广泛使用的中学生拓扑游戏。对宇宙形状的推测可以追溯到古代，但对宇宙拓扑的严肃数学研究始于1854年，当时黎曼提出将超球体作为宇宙学模型。拓扑学在19世纪末蓬勃发展，导致了各种可能的三维空间。1900年，天文学家卡尔·施瓦茨柴尔德将这些模型作为空间拓扑学的候选模型提交给德国天文学会，但考虑到当时可获得的观测数据有限，他只能得出结论，宇宙肯定比我们的银河系大得多。事实上，宇宙拓扑学作为一门观测科学几乎没有取得什么进展，直到1990年的S，当时COBE和WMAP卫星在宇宙微波背景辐射中发现了有限宇宙的迹象。然而，过去的十年是一个动荡的十年，为了适应1998年暗能量的发现，双曲模型的紧张工作让位于平面和球面模型。最近，剧情出现了新的转折，宇宙微波背景的特征--以及一些光学和射电异常--都与处女座的方向一致。这表明了一些新的物理效应--也许是暗物质--这是以前没有解释过的。本项目的研究部分将几何和拓扑知识应用于正在进行的理解我们宇宙的形状和本质的努力中，而教育部分使这些令人惊叹的美丽想法能够为中学生、高中生和大学生所接受(www.geometrygames.org)。