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.

Highlights

  • AND MOTIVATIONEinstein’s theory of general relativity (GR) exists in different versions

  • We first proposed a set of criteria for systematically constructing a theory of matter coupled to EC gravity and we included in the action all terms that fulfill these criteria

  • On we solely focus on EC gravity coupled nonminimally to a real scalar field, which we denote by h

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Summary

INTRODUCTION

Einstein’s theory of general relativity (GR) exists in different versions. Along with the most commonly used metric approach, these include the Palatini, affine, and teleparallel formulations, as well as Einstein-Cartan gravity. To achieve global scale invariance and to yield an acceptable cosmological and particle physics phenomenology, the model necessitates the presence of yet another scalar field, the dilaton, a singlet under the SM symmetries. Weyl transformations affect nontrivially the Riemannian curvatures and torsion, and the latter transform in an inhomogeneous manner This implies that, at least in principle, it is possible to make the theory invariant under gauged scale transformations without introducing new degrees of freedom, but rather by employing quantities of geometric origin that in any case are already present.

Conventions
Criteria for constructing the action
Equivalent metric theory
SCALE INVARIANCE
The need for an additional dilaton
The Higgs-dilaton model in EC gravity
Zð1 þ ξhZÞ3
Inclusion of fermions
General action
CONCLUSIONS
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