Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature (R) and in the Weyl tensor (C sigma) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field becomes massive (mass m approximate to Planck scale) after eating the dilaton in the R-2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field . Below m this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a low-energy limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field phi(1) (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling 1 phi 12 R to Weyl geometry, with Higgs mass (1)/(0) ((0) is the coefficient of the R-2 term). In realistic models (1) must be classically tuned (1) << (0). We comment on the quantum stability of this value.