Frozen up Dilaton and the GUT/Planck Mass Ratio

Understand

By treating modulus and phase on equal footing, as prescribed by Dirac, local scale invariance can consistently accompany any Brans-Dicke $\omega$-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)$^2$s.