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, r ∼ l exp[(4π)3/g2], 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 m ∼ 1/(M pr2) is stable under radiative corrections. For 1/r ∼ 10-3 eV the radion is extremely light, m ∼ 10-33 eV. Its couplings cause important deviations from general relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.