Theoretical Cosmology and Higher Dimensional Gravity

我将研究更高维度的引力。我将改进高维Weyl张量的代数分类，目的是获得(洛伦兹)度量的真正正则形式。我将寻求任意维度的经典和量子修正广义相对论和超重力的精确解。我已经从四个维度证明了(所谓的)非简并Kundt时空可以用它的标量多项式曲率不变量(SPCI)唯一地刻画。我将第一次确定SPCI的基础。我将寻找一种更实用的方法来确定使用SPCI的高维时空的代数类型。我将在代数上分类并寻找新的精确的高维黑洞解。我将定性地研究宇宙学模型(使用动力系统理论)，并约束来自弦理论和高维理论的暴涨模型。我将研究非均匀的宇宙学模型。我将研究宇宙学中的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反作用的影响。我将研究黑洞是否能够在一个重新塌陷然后反弹到新的膨胀阶段的宇宙中持续存在。我将研究尖峰对大尺度结构形成的影响(我们最近发现，尖峰是在早期宇宙的广义相对论范围内自然发生的)。

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.