Scale and Weyl Invariance in Einstein-Cartan Gravity

TL;DR

This paper demonstrates how Einstein-Cartan gravity can be extended to include both global and local scale invariance, leading to new models with potential implications for particle physics and cosmology.

Contribution

It constructs a broad class of Einstein-Cartan models with nonpropagating torsion and nonminimal scalar coupling that realize scale and Weyl invariance, clarifying their phenomenological relevance.

Findings

Models with nonpropagating torsion and scalar fields exhibit scale invariance.

Weyl invariance eliminates the need for a dilaton, simplifying the model.

Equivalent metric theories are derived for both invariance scenarios.

Abstract

We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagaing torsion and a nonminimally coupled scalar field. In phenomenological applications the scalar field is associated with the Higgs boson. For global scale invariance, an additional field -- dilaton -- is needed to make the theory phenomenologically viable. In the case of the Weyl symmetry, the dilaton is spurious and the theory reduces to a sub-class of one-field models. In both scenarios of scale invariance, we derive an equivalent metric theory and discuss possible implications for phenomenology.