Theoretical Cosmology and Higher Dimensional Gravity

我将研究更高维度的重力。我将改进Weyl张量在高维中的代数分类，目的是获得（洛伦兹）度量的真规范形式。我将在任意维度上寻找经典和量子修正广义相对论和超引力的精确解。我已经证明了在四维空间中，一个（所谓的）非简并的昆特时空可以用它的标量多项式曲率不变量（SPCI）来唯一表征。我将第一次确定SPCI的基础。我将寻求一种更实用的方法来确定一个高维时空的代数类型，使用SPCI。我将进行代数分类并寻求新的高维黑洞精确解。我将定性地研究宇宙模型（使用动力系统理论），并从弦理论和高维理论中约束暴胀模型。我将研究非齐次宇宙模型。我将研究空间不均匀性和空间曲率在宇宙学中的影响（通过微扰理论中的反作用）。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在一个重新坍缩然后弹跳进入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自然而普遍地发生）对大尺度结构形成的影响。

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.