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The Compactification Problems of Additional Dimensions in Multidimensional Cosmological Theories

Multidimensionality of our Universe is one of the most intriguing assumption in modern physics. It follows naturally from theories unifying different fundamental interactions with gravity, e.g. M/string theory. The idea has received a great deal of renewed attention over the last few years. However, it also brings a row of additional questions. According to observations the internal space should be static or nearly static at least from the time of primordial nucleosynthesis, otherwise the fundamental physical constants would vary. This means that at the present evolutionary stage of the Universe there are two possibilities: slow variation or compactification of internal space scale parameters. In many recent studies the problem of extra dimensions stabilization was studied for so-called ADD. Under these approaches a massive scalar fields (gravitons or radions) of external space-time can be presented as conformal excitations. In above mentioned works it was assumed that multidimensional action to be linear with respect to curvature. Although as follows from string theory, the gravity action needs to be extended to nonlinear one. In order to investigate effects of nonlinearity, in this Thesis a multidimensional Lagrangian will be studied, having the form L = f(R), where f(R) is an arbitrary smooth function of the scalar curvature.