Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions

Abstract

General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity, we employ metric-affine gravity, which encompasses as special cases the metric, Palatini, Einstein-Cartan and Weyl formulations. We first discuss the interaction of fermions with torsion and non-metricity, also commenting on projective symmetry. With a view towards the Standard Model, we then construct a generic model of (complex) scalar, fermionic and gauge fields coupled to GR and derive an equivalent metric theory, which features numerous new interaction terms. As a first observable consequence, we point out that a gravitational mechanism for producing dark matter in the form of singlet fermions can be used to distinguish between metric gravity and other formulations of GR.

54 pages, 3 appendices; v2: small improvements and moved some material from main part to appendices, matches published version (up to references)

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• The Standard Model Higgs boson as the inflaton
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Sterile Neutrinos as the Origin of Dark and Baryonic Matter
• The nuMSM, leptonic asymmetries, and properties of singlet fermions
• Higgs-Palatini Inflation and Unitarity
• The Present and Future Status of Heavy Neutral Leptons
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• The Higgs Phenomenon in Quantum Gravity
• Torsion Cosmology and the Accelerating Universe
• Preheating in Palatini Higgs inflation
• Metric-affine Gravity and Inflation
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Barbero-Immirzi field in canonical formalism of pure gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
• Infrared quantum information
• Metric-Affine Gravity as an Effective Field Theory
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Inflation in Metric-Affine Quadratic Gravity
• Immirzi parameter and fermions with non-minimal coupling
• Matter-antimatter asymmetry and dark matter from torsion
• Cosmological dynamics with propagating Lorentz connection modes of spin zero
• The particle spectrum of parity-violating Poincaré gravitational theory
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Quintessential inflation in Palatini $f(R)$ gravity
• Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms
• Dark matter as a Weyl geometric effect
• Palatini $R^2$ Quintessential Inflation
• Matter matters in Einstein-Cartan gravity
• Higgs inflation and teleparallel gravity
• Critical point Higgs inflation in the Palatini formulation
• Generalized plane waves in Poincaré gauge theory of gravity
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• Modified gravity: a unified approach to metric-affine models
• Remarks on Barbero-Immirzi parameter as a field
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• The dark side of the torsion: Dark Energy from propagating torsion
• Electroweak vacuum decay in metric-affine gravity
• Nonmetricity theories and aspects of gauge symmetry
• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Multiple point criticality principle and Coleman-Weinberg inflation
• Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Compact stellar structures in Weyl geometric gravity
• Stability of non-degenerate Ricci-type Palatini theories
• Extended interactions in the Palatini-$R^2$ inflation
• The Timescales of Quantum Breaking
• Geometric Proca with Matter in Metric-Palatini Gravity
• Describing metric-affine theories anew: alternative frameworks, examples and solutions
• Geometrical Trinity of Unimodular Gravity
• Gravitational corrections to electroweak vacuum decay: metric vs. Palatini
• Constant-Roll Inflation in modified $f(R,\varphi )$ gravity model using Palatini Formalism
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Conformal Metric-Affine Gravities
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Non-perturbative production of fermionic dark matter from fast preheating
• Sources of torsion in Poincare gauge theory
• Spontaneous scale symmetry breaking at high temperature

Cited by in corpus (11)

• Preheating in Einstein-Cartan Higgs Inflation: Oscillon formation
• Inflation in Weyl-invariant Einstein-Cartan gravity
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• General Einstein-Cartan quadratic gravity with derivative couplings
• $\tilde{\xi }$-attractors in metric-affine gravity
• Effect of Torsion on Neutron Star Structure in Einstein-Cartan Gravity
• Friedmann cosmology with hyperfluids
• Radiative corrections to the $R$ and $R^2$ invariants from torsion fluctuations on maximally symmetric spaces
• Ephemeral Oscillons in Scalar-Tensor Theories: The Higgs-like case
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• Equivalence of first and second order formulations of the Einstein-Hilbert theory