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Multidimensionality of our Universe is one of the most intriguing assumptionin modern physics. It follows naturally from theories unifying differentfundamental interactions with gravity, e.g. M/string theory. The idea hasreceived a great deal of renewed attention over the last few years. However, italso brings a row of additional questions. According to observations theinternal space should be static or nearly static at least from the time ofprimordial nucleosynthesis, otherwise the fundamental physical constants wouldvary. This means that at the present evolutionary stage of the Universe thereare two possibilities: slow variation or compactification of internal spacescale parameters. In many recent studies the problem of extra dimensionsstabilization was studied for so-called ADD. Under these approaches a massivescalar fields (gravitons or radions) of external space-time can be presented asconformal excitations. In above mentioned works it was assumed thatmultidimensional action to be linear with respect to curvature. Although asfollows from string theory, the gravity action needs to be extended tononlinear one. In order to investigate effects of nonlinearity, in this Thesisa multidimensional Lagrangian will be studied, having the form L = f(R), wheref(R) is an arbitrary smooth function of the scalar curvature.

The Compactification Problems of Additional Dimensions in Multidimensional Cosmological Theories