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Scale and Weyl Invariance in Einstein-Cartan Gravity

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arxiv 2108.05897 v2 pith:FIYPEAUH submitted 2021-08-12 hep-th gr-qchep-ph

Georgios K. Karananas , Mikhail Shaposhnikov , Andrey Shkerin , Sebastian Zell This is my paper
classification hep-thgr-qchep-ph
keywords scaleinvariancefieldtheoryweyldilatoneinstein-cartanglobal
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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.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Gravitational Origin of the QCD Axion

    hep-th 2025-06 accept novelty 7.0 of 10

    Derivative-coupled gravitational axions cannot solve the strong CP problem; Weyl-invariant Einstein-Cartan gravity is identified as the only promising framework for a gravitational QCD axion.

  2. Weyl-invariant Einstein-Cartan gravity with a heavy ALP: Higgs Inflation and $\alpha$-attractors

    hep-ph 2025-07 conditional novelty 6.0 of 10

    In a Weyl-invariant Einstein-Cartan gravity theory with the SM Higgs and a heavy gravitational ALP, tuning two nonminimal couplings reproduces metric Higgs inflation and α-attractor-like inflation with ns≈1−2/N and r≈12/N^2.

  3. The Goldstone Awakens: Unimodular dark energy in scale-invariant $R^2$ gravity

    astro-ph.CO 2026-07 conditional novelty 5.0 of 10

    In a scale-invariant R² + unimodular-gravity model, the Goldstone boson of scale symmetry becomes thawing dark energy, with its equation of state fixed by the same coupling that sets the inflationary spectral tilt.

  4. Atomic clocks and gravitational waves as probes of non-metricity

    gr-qc 2026-01 reject novelty 5.0 of 10

    The paper claims existing gravitational-wave data already bound Weyl non-metricity, α²ω̄0<10⁻⁶⁹ GeV, via backreaction of a Planck-scale Weyl field, but a dropped kinetic term numerically exceeds the assumed sensitivity.

  5. Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models

    gr-qc 2025-12 conditional novelty 5.0 of 10

    Adding cubic Holst-invariant terms to F(R,R̃) Einstein-Cartan inflation models systematically lowers the predicted spectral index n_s and tensor-to-scalar ratio r, restoring data compatibility in parameter regions whe...

  6. Progress in Einstein-Cartan gravity

    hep-th 2025-06 conditional novelty 3.0 of 10

    A review of Weyl-invariant Einstein-Cartan gravity claiming that one extra axion-like scalar can unify the strong CP and hierarchy puzzles, with the hierarchy explained by tiny Lorentz gauge couplings.

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