Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance

Recently, it has been pointed out that dimensionless actions in four dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed {\it restricted Weyl invariance}. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein-Hilbert action with cosmological constant and a Higgs mass. The model also contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling $R Φ^2$ between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the standard model can be incorporated into the original restricted Weyl invariant action.

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