Weyl gauge symmetry and its spontaneous breaking in the standard model and inflation

We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the standard model (SM) and inflation. In models with nonminimal couplings of the scalar fields to the Ricci scalar that are conformal invariant, the spontaneous generation by a scalar field (s) vacuum expectation value of a positive Newton constant demands a negative kinetic term for the scalar field or vice versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field _ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field _ undergoes a Stueckelberg mechanism and becomes massive after ``eating'' the (radial mode) would-be Goldstone field (dilaton) in the scalar sector. Before the decoupling of _, the dilaton can act as an UV regulator and maintain the Weyl symmetry at the quantum level, with relevance for solving the hierarchy problem. After the decoupling of _, the scalar potential depends only on the remaining (angular variables) scalar fields, which can be the Higgs field, inflaton, etc. We show that a successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with _ introduced to avoid ghosts, the natural framework is that of Weyl geometry, which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.