Abstract

We put forward the idea that in addition to invariance under coordinate transformations of general relativity (GR) the gravitational interaction is invariant under arbitrary scale deformations of the metric field, as well as other fields. In addition, we assume that the scaling field has an internal symmetry. Because scale invariance is imposed only on gravity, while the standard model (SM) retains its usual non-Weyl-invariant form, the full framework is not merely a rewriting of GR plus the SM. The global charges that are associated with the internal symmetry could potentially source the gravitational field. Throughout, the framework is treated as a classical generalization of GR on sufficiently sub-Planckian energies; accordingly, any discussion of global charges is to be understood within this effective classical domain. In the case that isotropic deformations are considered, the theory reduces to a Weyl-invariant scalar–tensor (WIST) version of GR. In case that the reference metric is chosen to be Minkowski, the metric factorization takes the standard vierbein form, apart from the additional internal structure assumed here. A few other implications of WIST are considered as well.

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