Theoretical Cosmology and Higher Dimensional Gravity

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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.