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We consider the (gauged) Weyl gravity action, quadratic in the scalarcurvature ($\tilde R$) and in the Weyl tensor ($\tilde C_{\mu\nu\rho\sigma}$)of the Weyl conformal geometry. In the absence of matter fields, this actionhas spontaneous breaking in which the Weyl gauge field $\omega_\mu$ becomesmassive (mass $m_\omega\sim$ Planck scale) after "eating" the dilaton in the$\tilde R^2$ term, in a Stueckelberg mechanism. As a result, one recovers theEinstein-Hilbert action with a positive cosmological constant and the Procaaction for the massive Weyl gauge field $\omega_\mu$. Below $m_\omega$ thisfield decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbertaction is then just a "low-energy" limit of Weyl quadratic gravity which thusavoids its previous, long-held criticisms. In the presence of matter scalarfield $\phi_1$ (Higgs-like), with couplings allowed by Weyl gauge symmetry,after its spontaneous breaking one obtains in addition, at low scales, a Higgspotential with spontaneous electroweak symmetry breaking. This is induced bythe non-minimal coupling $\xi_1\phi_1^2 \tilde R$ to Weyl geometry, with Higgsmass $\propto\xi_1/\xi_0$ ($\xi_0$ is the coefficient of the $\tilde R^2$term). In realistic models $\xi_1$ must be classically tuned $\xi_1\ll \xi_0$.We comment on the quantum stability of this value.

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