On winding branes and cosmological evolution of extra dimensions in string theory

We consider evolution of compact extra dimensions in cosmology and try to see whether wrapped branes can prevent the expansion of the internal space. Some difficulties of the Brandenberger and Vafa mechanism for decompactification are pointed out. In both pure Einstein and dilaton gravities, we study cosmology of winding brane gases in a continuum approximation. The energy-momentum tensor is obtained by coupling the brane action to the gravity action and we present several exact solutions for various brane configurations. T-duality invariance of the solutions is established in dilaton gravity. Our results indicate that phenomenologically the most viable scenario can be realized when there is only one brane wrapping over all extra dimensions.