Inflation from extra dimensions

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 $V\left(b\right)\mathrm{}$ with a simple polynomial form, to get the observed density perturbations, the energy scale of $V\left(b\right)\mathrm{}$ must greatly exceed $M\sim 1\hspace{0.5em}\mathrm{TeV}:\hspace{0.5em}{V\left(b\right)\mathrm{}}^{1/4}\equiv M_V\sim {10}^{-4}{M}_P.$ This gives a large radion mass and reheat temperature $\sim {10}^9\hspace{0.5em}\mathrm{GeV},$ 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 bulk matter fields rather than by the radion.