D-branes, string cosmology, and large extra dimensions

D-branes are fundamental in all scenarios where there are large extra dimensions and the string scale is much smaller than the four-dimensional Planck mass. We show that this current picture predicts a period of inflation on our brane which is driven by the large extra dimensions and the issue of the graceful exit becomes inextricably linked to the problem of the stabilization of the extra dimensions, suggesting the possibility of a common solution. We also show that branes may violently fluctuate along their transverse directions in curved spacetime, possibly leading to a period of brane-driven inflation. This phenomenon plays also a crucial role in many other cosmological issues, such as the smoothing out of the cosmological singularities.