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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568599
• 关键词: Theoretical; Cosmology; Higher; Dimensional; Gravity

I will investigate higher dimensional gravity. I will refine the algebraic classification of the Weyl tensor in higher dimensions with the object of obtaining true canonical forms for (Lorentzian) metrics. I shall seek exact solutions of classical and quantum corrected general relativity and supergravity in arbitrary dimensions. I have proven in four dimensions that a (so-called) non-degenerate Kundt spacetime can be uniquely characterized by its scalar polynomial curvature invariants (SPCI). I will determine, for the first time, a basis of SPCI. I will seek a more practical way of determining the algebraic type of a higher dimensional spacetime employing SPCI. I will algebraically classify and seek new exact higher dimensional black hole solutions. I will study cosmological models qualitatively (using dynamical systems theory), and constrain models of inflation inspired from string theory and higher-dimensional theories. I will study inhomogeneous cosmological models. I will investigate the effects of spatial inhomogeneities and spatial curvature in cosmology (through backreaction effects in perturbation theory). I propose to study the effect of non-Gaussianities on backreaction. I shall investigate whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. I will study the effect of spikes (that we have recently found to occur naturally and generically within general relativity in the early universe) on the formation of large scale structure.

我将研究更高维度的引力。 我将完善代数 韦尔张量在更高维度的分类，目的是获得真实的 （洛伦兹）度量的规范形式。 我将寻求经典和 量子修正了任意维度的广义相对论和超引力。 我有 在四个维度上证明了（所谓的）非简并昆特时空可以是 其独特之处在于其标量多项式曲率不变量（SPCI）。 我会 首次确定了SPCI的基础。 我会寻求更实际的方法 使用 SPCI 确定高维时空的代数类型。 我会 代数分类并寻找新的精确的高维黑洞解决方案。 我将定性地研究宇宙学模型（使用动力系统理论），并且 受弦理论和高维启发的膨胀约束模型 理论。 我将研究非齐次宇宙学模型。 我将调查 宇宙学中空间不均匀性和空间曲率的影响（通过 微扰理论中的反反应效应）。 我建议研究一下效果 反反应的非高斯性。 我将研究黑洞是否可以 持续存在于宇宙中，宇宙会重新塌缩，然后弹回新的膨胀阶段。 我 将研究尖峰的影响（我们最近发现它是自然发生的，并且 一般在早期宇宙的广义相对论中）关于大的形成 规模结构。