Theoretical Cosmology and Higher Dimensional Gravity

我将研究更高维度的引力。我会改进代数 以求真为目的的高维Weyl张量分类 (洛伦兹)度量的典范形式。我将寻求经典和经典问题的精确解 量子修正了任意维度的广义相对论和超重力。我有过 从四个维度证明了(所谓的)非简并昆特时空 它的唯一特征是它的标量多项式曲率不变量(SPCI)。这就做 第一次确定了SPCI的基础。我会寻找一种更实际的方法来 使用SPCI确定高维时空的代数类型。这就做 代数分类和寻找新的精确的高维黑洞解。 我将定性地研究宇宙模型(使用动力系统理论)，以及 由弦理论和高维理论启发的约束膨胀模型 理论。我将研究非均匀的宇宙学模型。我会调查 宇宙学中的空间不均匀和空间曲率的影响(至 微扰理论中的反向反应效应)。我建议研究一下 关于反作用的非高斯主义。我将调查黑洞是否可以 坚持在一个重新塌陷的宇宙中，然后反弹到新的扩张阶段。我 将研究尖峰的影响(我们最近发现尖峰是自然发生的，并且 一般在早期宇宙的广义相对论范围内)的形成 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.