ADIABATIC PERTURBATIONS AND MINIMAL SIZE OF THE DESITTER VACUUM

We consider transitions for a higher dimensional to a lower dimensional de Sitter phase. We show that, if the transitions are adiabatic, the evolution necessarily passes through a state of maximal curvature (minimal size). This minimal size depends only on the total entropy content, but the dependence is so weak that no fine tuning is needed in order to set the minimum at the Planck scale.