Exponentially large extra dimensions

We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii that are naturally exponentially large, rsimilar tol exp[(4pi)(3)/g(2)], where l is a microscopic physics scale and g is the (dimensionless) cubic coupling constant. The resulting radion mode of the metric becomes a very light degree of freedom whose mass msimilar to1/(M(p)r(2)) is stable under radiative corrections. For 1/rsimilar to10(-3) eV the radion is extremely light, msimilar to10(-33) eV. Its couplings cause important deviations from general relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.