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.

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

References in corpus (24)

• Cosmology and the Fate of Dilatation Symmetry
• The Standard Model Higgs boson as the inflaton
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Scale invariance, unimodular gravity and dark energy
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Barbero-Immirzi field in canonical formalism of pure gravity
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
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• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Higgs inflation with the Holst and the Nieh-Yan term
• Quantum Effects in Palatini Higgs Inflation
• No fifth force in a scale invariant universe
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Immirzi parameter and fermions with non-minimal coupling
• Higgs inflation in Einstein-Cartan gravity
• The particle spectrum of parity-violating Poincaré gravitational theory
• Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation
• Einstein-Cartan Portal to Dark Matter
• Sub-Planckian ${\varphi }^2$ Inflation in the Palatini Formulation of Gravity with an $R^2$ term
• Remarks on Barbero-Immirzi parameter as a field
• Fundamental Scale Invariance
• One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry
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Cited by in corpus (29)

• Palatini-Higgs inflation with non-minimal derivative coupling
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Tachyonic Preheating in Palatini $R^2$ Inflation
• 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
• Cosmology from pregeometry
• Pregeometry and euclidean quantum gravity
• Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity
• 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
• Spontaneous scale symmetry breaking at high temperature
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• 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