On cosmologically induced hierarchies in string theory

We propose, within a perturbative string theory example, a cosmological way to generate a large hierarchy between the observed Planck mass and the fundamental string scale. Time evolution results in three large space dimensions, one additional dimension transverse to our world and five small parallel compact dimensions with a very slow time evolution. The string coupling becomes asymptotically very small generating a large Planck mass. However due to an exact compensation between the time evolution of the internal space and that of the string coupling, the Yang-Mills gauge couplings on our Universe are time independent and of order one