  The radial mode of n extra compact dimensions (the radion, b) can cause
inflation in theories where the fundamental gravity scale, M, is smaller than
the Planck scale M_P. For radion potentials V(b) with a simple polynomial form,
to get the observed density perturbations, the energy scale of V(b) must
greatly exceed M ~ 1 TeV: V(b)^{1/4} = M_v ~ 10^{-4} M_P. This gives a large
radion mass and reheat temperature ~ 10^9 GeV, thus avoiding the moduli
problem. Such a value of M_v can be consistent with the classical treatment if
the new dimensions started sufficiently small. A new possibility is that b
approaches its stable value from above during inflation. The same conclusions
about M_v may hold even if inflation is driven by matter fields rather than by
the radion.
