Higher‐Dimensional Unification and Dilatonic Dark Matter

We discuss the physical implications of the extra space in higher‐dimensional unification, and show that a large extra space requires an extremely small fine structure constant (of the order of $10−42$⁠) for the Kaluza‐Klein gauge boson, or else a huge violation of equivalence principle in 4‐dimensional Einstein gravity. More importantly, the extra space generates the dilaton which represents the volume element of the extra space. We show that the scalar curvature of the extra space generates the dilaton mass, and that the dilaton mass determines the size of the extra space. Moreover, as a massive scalar graviton, the dilaton can be an excellent candidate of dark matter. Assuming that the dilaton is the dark matter, we estimate the lower bound of the scale of the extra space to be of $10−42m.$