Theoretical Cosmology and Higher Dimensional Gravity

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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.