Wrapped branes and compact extra dimensions in cosmology

We present a cosmological model in 1+m+p dimensions, where in m-dimensional space there are uniformly distributed p-branes wrapping over the extra p dimensions. We find that during cosmological evolution m-dimensional space expands with the exact power-law corresponding to pressureless matter while the extra p dimensions contract. Adding matter, we also obtain solutions having the same property. We show that this might explain in a natural way why the extra dimensions are small compared to the observed three spatial directions.