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We discuss the local (gauged) Weyl symmetry and its spontaneous breaking andapply it to model building beyond the Standard Model (SM) and inflation. Inmodels with non-minimal couplings of the scalar fields to the Ricci scalar,that are conformal invariant, the spontaneous generation by a scalar field(s)vev of a positive Newton constant demands a negative kinetic term for thescalar field, or vice-versa. This is naturally avoided in models withadditional Weyl gauge symmetry. The Weyl gauge field $\omega_\mu$ couples tothe scalar sector but not to the fermionic sector of a SM-like Lagrangian. Thefield $\omega_\mu$ undergoes a Stueckelberg mechanism and becomes massive after"eating" the (radial mode) would-be-Goldstone field (dilaton $\rho$) in thescalar sector. Before the decoupling of $\omega_\mu$, the dilaton can act as UVregulator and maintain the Weyl symmetry at the {\it quantum} level, withrelevance for solving the hierarchy problem. After the decoupling of$\omega_\mu$, the scalar potential depends only on the remaining (angularvariables) scalar fields, that can be the Higgs field, inflaton, etc. We showthat successful inflation is then possible with one of these scalar fieldsidentified as the inflaton. While our approach is derived in the Riemanniangeometry with $\omega_\mu$ introduced to avoid ghosts, the natural framework isthat of Weyl geometry which for the same matter spectrum is shown to generatethe same Lagrangian, up to a total derivative.

Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation