Theoretical Cosmology and Higher Dimensional Gravity

我将研究更高维度的引力。 我会完善代数 分类的外尔张量在更高的维度与目标，获得真正的 （Lorentzian）Metrics的标准形式。 我将寻求古典和 量子修正了广义相对论和任意维度的超引力。 我有 在四维空间中证明了一个（所谓的）非简并的孔特时空可以是 其唯一特征在于其标量多项式曲率不变量（SPCI）。 我会 第一次确定SPCI的基础。 我会寻找一个更实际的方法 使用SPCI确定高维时空的代数类型。 我会 代数分类和寻求新的精确高维黑洞的解决方案。 我将研究宇宙模型定性（使用动力系统理论）， 从弦理论和高维空间中得到启发的暴胀的约束模型 理论 我将研究非均匀宇宙模型。 我会调查 宇宙学中空间不均匀性和空间曲率的影响（通过 微扰理论中的反向反应效应）。 我建议研究 逆反应的非高斯性 我将研究黑洞是否能 在一个宇宙中持续存在，这个宇宙经历了短暂的衰退，然后反弹到一个新的膨胀阶段。 我 将研究尖峰的影响（我们最近发现自然发生， 广义相对论中的早期宇宙）的形成大 规模结构

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.