Inflation and Large Internal Dimensions
  We consider some aspects of inflation in models with large internal dimensions. If inflation occurs on a 3D wall after the stabilization of internal dimensions in the models with low unification scale (M ~ 1 TeV), the inflaton field must be extremely light. This problem may disappear In models with intermediate (M ~10^{11} GeV) to high (M ~ 10^{16} GeV) unification scale. However, in all of these cases the wall inflation does not provide a complete solution to the horizon and flatness problems. To solve them, there must be a stage of inflation in the bulk before the compactification of internal dimensions. 
Nemanja Kaloper and Andrei Linde