Inhomogeneous multidimensional cosmological models with a higher dimensional space-are investigated under dimensional reduction to tensor-multi-scalar theories. In the Einstein conformal frame, these theories take the shape of a flat σ-model. For the singular case where M 0 is 2-dimensional, the dimensional reduction to dilaton gravity is preformed with different distinguished representations of the action. PACS number(s): 04.50.+h, 98.80.Hw, 04.60.Kz 1 This work was financially supported by DFG grants 436 RUS 113/7/0, 436 UKR 17/7/95, and the DAAD.

Inhomogeneous multidimensional cosmological models with a higher dimen-are investigated under dimensional reduction to a D 0 -dimensional effective non-minimally coupled σ-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Einstein frame reformulation of known solutions in the Brans-Dicke frame is given. As an example, the reformulation is demonstrated explicitly for the generalized Kasner solutions where it is shown that in the Einstein frame there are no solutions with inflation of the external space. 04.50.+h, 98.80.Hw

We consider a D-dimensional self-gravitating spherically symmetric configuration of a generalized electro-magnetic n-form F and a dilatonic scalar field, admitting an interpretation in terms of intersecting p-branes. For theories with multiple times, selection rules are obtained, which obstruct the existence of p-branes in certain subspaces. General static solutions are obtained under a specific restriction on the model parameters, which corresponds to the known "intersection rules". More special families of solutions (with equal charges for some of the F -field components) are found with weakened restrictions on the input parameters. Black-hole solutions are determined, and it is shown that in the extreme limit the Hawking temperature may tend to zero, a finite value, or infinity, depending on the p-brane intersection dimension. A kind of no-hair theorem is obtained, claiming that black holes cannot coexist with a quasiscalar component of the F -field.

For multi-dimensional cosmological models we investigate the dynamics of both, scales and dimensions. The classical equation of motions and the corresponding Wheeler-de Witt equation are set up generally and the qualitative behaviour of the system is discussed for some specific model. with 2 factor spaces: A space M I with dynamical dimension, and a compact internal space MZ of constant dimension. With a natural choice of some contraint, there exist a solution where M I expands as usual space while Mz is shrinking down to unobservable scales.Key words: cosmology: higher dimensions -dynamical dimensions -Wheeler-deWitt equation AAA subject classification: 161 IntroductionMost modern cosmological scenarios contain a regime at early times which is well described by a multi-dimensional cosmological model. Here we continue a series of recent investigations (Bleyer et al. (1990a), Bleyer et al. (1990b, Bleyer and Zhuk (1994), Bleyer et al. (1994), Bleyer et al. (1995), Rainer (1995) of such models. While usually the dimension di of each factor space Mi is assumed to be a natural number, here it is, more generally, allowed to be a smooth function of time. As in the usual case, also for fractal factor spaces Mi their scale factors ai are dynamical. Hence the classical dynamical variables are the scale factor exponents p" = In ai, their derivatives, and the fractal dimensions di of the factor spaces Mi.Such a model is actually motivated by the observed correlation function of galaxy clusters and the fluctuation of microwave background radiation. Both seem to have fractal structure (Luo and Schramm (1992), De Gouveia Dal Pino et al. (1995)). These kinds of observations suggest to attribute a fractal structure to the universe. When the building blocks of space-time or some of its subspaces have a fractal structure, its dimension may have a noninteger value.The idea that a space-time might have a variable noninteger dimension, was suggested also by Hochberg and Wheeler (1991