Zhuk O. Multidimensional classical and quantum cosmology

The dissertation is devoted to problems of the multidimensional classical and quantum cosmology which represents a new direction in the field of origin and evolution of the universe. Classes of new exact solutions of the classical Einstein equations and the quantum Wheeler-DeWitt equations are obtained. They describe the behaviour of the multidimensional universe. Conditions for stable compactification of the internal dimensions near the Planck scales and effective four-dimensionality of the multidimensional universe are found. It is shown that conformal excitations of the stably compactified internal spaces can be observed as massive scalar fields - gravitational excitons in the external space-time. The models where the multidimensional universe effectively behaves in accordance with the Friedmann model are constructed. It shows a principled possibility of the extra dimensions existence. K