Scale and Weyl Invariance in Einstein-Cartan Gravity

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.

Journal version---discussion extended, typos corrected, references added

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• Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms
• The origin of Weyl gauging in metric-affine theories
• Projective transformations in metric-affine and Weylian geometries
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