  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 leads to a new approach to
string cosmology where inflation on our brane 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 and the generation of the baryon asymmetry on
our three brane.
