Abstract
We introduce Weyl's scale symmetry into the standard model as a local symmetry. This necessarily introduces gravitational interactions in addition to the local scale invariance group $\stackrel{\texttildelow{}}{U}(1)$ and the standard model groups $SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$. The only other new ingredients are a new scalar field $\ensuremath{\sigma}$ and the gauge field for $\stackrel{\texttildelow{}}{U}(1)$ we call the Weylon. A noteworthy feature is that the system admits the St\"uckelberg-type compensator. The $\ensuremath{\sigma}$ couples to the scalar curvature as $(\ensuremath{-}\ensuremath{\zeta}/2){\ensuremath{\sigma}}^{2}R$ and is in turn related to a St\"uckelberg-type compensator $\ensuremath{\varphi}$ by $\ensuremath{\sigma}\ensuremath{\equiv}{M}_{\mathrm{P}}{e}^{\ensuremath{-}\ensuremath{\varphi}/{M}_{\mathrm{P}}}$ with the Planck mass ${M}_{\mathrm{P}}$. The particular gauge $\ensuremath{\varphi}=0$ in the St\"uckelberg formalism corresponds to $\ensuremath{\sigma}={M}_{\mathrm{P}}$, and the Hilbert action is induced automatically. In this sense, our model presents yet another mechanism for breaking scale invariance at the classical level. We show that our model naturally accommodates the chaotic inflation scenario with no extra field.
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