The radial mode ofnextra compact dimensions (the radion,b) can cause inflation in theories where the fundamental gravity scale,M, is smaller than the Planck scaleMP.For radion potentialsV(b)with a simple polynomial form, to get the observed density perturbations, the energy scale ofV(b)must greatly exceedM∼1&hthinsp;TeV:&hthinsp;V(b)1/4≡MV∼10−4MP.This gives a large radion mass and reheat temperature∼109&hthinsp;GeV,thus avoiding the moduli problem. Such a value ofMVcan be consistent with the classical treatment if the new dimensions started sufficiently small. A new possibility is thatbapproaches its stable value from above during inflation. The same conclusions aboutMVmay hold even if inflation is driven by matter fields rather than by the radion. ©1999 American Institute of Physics.