  In the context of (4+d)-dimensional general relativity, we propose an
inflationary scenario wherein 3 spatial dimensions grow large, while d extra
dimensions remain small. Our model requires that a self-interacting d-form
acquire a vacuum expectation value along the extra dimensions. This causes 3
spatial dimensions to inflate, whilst keeping the size of the extra dimensions
nearly constant. We do not require an additional stabilization mechanism for
the radion, as stable solutions exist for flat, and for negatively curved
compact extra dimensions. From a four-dimensional perspective, the radion does
not couple to the inflaton; and, the small amplitude of the CMB temperature
anisotropies arises from an exponential suppression of fluctuations, due to the
higher-dimensional origin of the inflaton. The mechanism triggering the end of
inflation is responsible, both, for heating the universe, and for avoiding
violations of the equivalence principle due to coupling between the radion and
matter.
