Frozen up dilaton and the GUT/Planck mass ratio

By treating modulus and phase on equal footing, as prescribed by Dirac, local scale invariance can consistently accompany any Brans-Dicke ω-theory. We show that in the presence of a soft scale symmetry breaking term, the classical solution, if it exists, cannot be anything else but general relativistic. The dilaton modulus gets frozen up by the Weyl-Proca vector field, thereby constituting a gravitational quasi-Higgs mechanism. Assigning all grand unified scalars as dilatons, they enjoy Weyl universality, and upon symmetry breaking, the Planck (mass)2 becomes the sum of all their individual (VEV)2s. The emerging GUT/Planck (mass)2 ratio is thus ∼ωgGUT2/4π.