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Einstein and Brans-Dicke frames in multidimensional cosmology. (English) Zbl 0976.83055

Cosmological consequences of the dimensional reduction of higher-dimensional space-time manifold to an effective non-minimally coupled sigma-model are investigated. Two frames are introduced: (1) Brans-Dicke frame with non-minimally coupled dilatonic scalar field given by the total internal space volume; (2) Einstein frame with all dilatonic scalar fields minimally coupled. First, a reduced effective theory is formulated in an arbitrary frame. Then, a general method for transformations between solutions in the Brans-Dicke and Einstein frame is given. As an example, the transformation is obtained explicitly for the generalized Kasner solutions. It is shown that the solutions in the Einstein frame imply no inflation of the external space although they can undergo deflation after the cosmic synchronous time inversion.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
83F05 Relativistic cosmology
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