Theoretical Cosmology and Higher Dimensional Gravity

理论宇宙学和高维引力

• 批准号: 8532-2013
• 负责人: Coley, Alan
• 金额: $ 1.82万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633070
• 关键词: Theoretical; Cosmology; Higher; Dimensional; Gravity

I will investigate higher dimensional gravity. I will refine the algebraicclassification of the Weyl tensor in higher dimensions with the object of obtaining truecanonical forms for (Lorentzian) metrics. I shall seek exact solutions of classical andquantum corrected general relativity and supergravity in arbitrary dimensions. I haveproven in four dimensions that a (so-called) non-degenerate Kundt spacetime can beuniquely characterized by its scalar polynomial curvature invariants (SPCI). I willdetermine, for the first time, a basis of SPCI. I will seek a more practical way ofdetermining the algebraic type of a higher dimensional spacetime employing SPCI. I willalgebraically classify and seek new exact higher dimensional black hole solutions.I will study cosmological models qualitatively (using dynamical systems theory), andconstrain models of inflation inspired from string theory and higher-dimensionaltheories. I will study inhomogeneous cosmological models. I will investigate theeffects of spatial inhomogeneities and spatial curvature in cosmology (throughbackreaction effects in perturbation theory). I propose to study the effect ofnon-Gaussianities on backreaction. I shall investigate whether black holes couldpersist in a universe which recollapses and then bounces into a new expansion phase. Iwill study the effect of spikes (that we have recently found to occur naturally andgenerically within general relativity in the early universe) on the formation of largescale structure.

我将研究更高维度的引力。我将完善代数分类的外尔张量在更高的维度与目标获得真正的规范形式（洛伦兹）度量。我将寻求经典和量子修正的广义相对论和超引力在任意维度的精确解。我在四维空间中证明了一个（所谓的）非退化的Kundt时空可以唯一地由它的标量多项式曲率不变量（SPCI）来刻画。我将首次确定SPCI的基础。我将寻求一个更实际的方法来确定代数类型的高维时空采用SPCI。我将用代数方法对高维黑洞进行分类并寻找新的精确解，我将定性地研究宇宙学模型（使用动力系统理论），并从弦理论和高维理论中得到暴胀的约束模型。我将研究非均匀宇宙模型。我将研究宇宙学中空间不均匀性和空间曲率的影响（通过微扰理论中的反作用效应）。我建议研究非高斯性对逆反应的影响。我将研究黑洞是否能在一个经历了短暂的坍缩然后又反弹到一个新的膨胀阶段的宇宙中持续存在。我将研究尖峰效应（我们最近发现，在早期宇宙的广义相对论中，尖峰效应是自然发生的）对大尺度结构形成的影响。