Einstein-Cartan gravity, matter, and scale-invariant generalization

Abstract

We study gravity coupled to scalar and fermion fields in the Einstein-Cartan framework. We discuss the most general form of the action that contains terms of mass dimension not bigger than four, leaving out only contributions quadratic in curvature. By resolving the theory explicitly for torsion, we arrive at an equivalent metric theory containing additional six-dimensional operators. This lays the groundwork for cosmological studies of the theory. We also perform the same analysis for a no-scale scenario in which the Planck mass is eliminated at the cost of adding an extra scalar degree of freedom. Finally, we outline phenomenological implications of the resulting theories, in particular to inflation and dark matter production.

arXiv comment18 pages; v2: Weyl transformation of the fermionic kinetic term and sign of 4-fermion interaction corrected; references added; matches published version (including erratum)

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• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
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• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• Einstein-Cartan Portal to Dark Matter
• Matter matters in Einstein-Cartan gravity
• Critical point Higgs inflation in the Palatini formulation
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• The dark side of the torsion: Dark Energy from propagating torsion
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Electroweak vacuum decay in metric-affine gravity
• Pregeometry and spontaneous time-space asymmetry
• Extended interactions in the Palatini-$R^2$ inflation
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• Pregeometry and euclidean quantum gravity
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• Einstein-Proca theory from the Einstein-Cartan formulation
• Axion gravitodynamics, Lense-Thirring effect, and gravitational waves
• Massless Preheating and Electroweak Vacuum Metastability
• Probing dark gauge boson via Einstein-Cartan portal
• Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
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• Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion
• Twisting inflation to sub-Planckian axion decay constants
• Fate of chiral symmetry in Riemann-Cartan geometry