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.

arXiv comment54 pages, 3 appendices; v2: small improvements and moved some material from main part to appendices, matches published version (up to references)

References in corpus (175)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Standard Model Higgs boson as the inflaton
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Sterile Neutrinos as Dark Matter
• The $\nu$MSM, Dark Matter and Baryon Asymmetry of the Universe
• Coincident General Relativity
• The $\nu$MSM, Dark Matter and Neutrino Masses
• A New Dark Matter Candidate: Non-thermal Sterile Neutrinos
• Universality Class in Conformal Inflation
• Physical Aspects of the Space-Time Torsion
• The role of sterile neutrinos in cosmology and astrophysics
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Sterile Neutrino Dark Matter
• A systematic approach to generalisations of General Relativity and their cosmological implications
• The Phenomenology of Right Handed Neutrinos
• Dark Matter, Baryogenesis and Neutrino Oscillations from Right Handed Neutrinos
• Gravitational Lorentz Force and the Description of the Gravitational Interaction
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Teleparallel Palatini theories
• Sterile Neutrinos as the Origin of Dark and Baryonic Matter
• The nuMSM, leptonic asymmetries, and properties of singlet fermions
• Gravitational Energy-Momentum Density in Teleparallel Gravity
• Metric-affine approach to teleparallel gravity
• Quantum Compositeness of Gravity: Black Holes, AdS and Inflation
• Quantum Gravity, Torsion, Parity Violation and all that
• Physical effects of the Immirzi parameter
• Higgs-Palatini Inflation and Unitarity
• The Present and Future Status of Heavy Neutral Leptons
• Multi-field Conformal Cosmological Attractors
• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Quantum Break-Time of de Sitter
• The Higgs Phenomenon in Quantum Gravity
• Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
• Ghosts in metric-affine higher order curvature gravity
• Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings
• Palatini inflation in models with an $R^2$ term
• Observable traces of non-metricity: new constraints on metric-affine gravity
• Inflation with $R^2$ term in the Palatini formalism
• Constraints on Space-Time Torsion from Hughes-Drever Experiments
• Torsion Cosmology and the Accelerating Universe
• General Teleparallel Quadratic Gravity
• Preheating in Palatini Higgs inflation
• Cosmology with a spin
• A New Class of Ghost and Tachyon Free Metric Affine Gravities
• Reheating in $R^2$ Palatini inflationary models
• Extended Gauss-Bonnet gravities in Weyl geometry
• Instabilities in Metric-Affine Theories of Gravity
• Planck scale black hole dark matter from Higgs inflation
• How to constrain warm dark matter with the Lyman $\alpha$ forest
• Metric-affine Gravity and Inflation
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Friedmann-like universes with torsion
• Status of non-Riemannian cosmology
• ARS Leptogenesis
• Barbero-Immirzi field in canonical formalism of pure gravity
• The masses of active neutrinos in the nuMSM from X-ray astronomy
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini
• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
• Higgs inflation with the Holst and the Nieh-Yan term
• Dynamically induced Planck scale and inflation in the Palatini formulation
• Scale transformations in metric-affine geometry
• Infrared quantum information
• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• Higgs inflation in the Palatini formulation with kinetic terms for the metric
• The Lyman-$\alpha$ forest as a diagnostic of the nature of the dark matter
• Quantum Effects in Palatini Higgs Inflation
• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Hamiltonian analysis of Poincaré gauge theory scalar modes
• Metric-Affine Gravity as an Effective Field Theory
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Attractor Behaviour in Multifield Inflation
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
• Inflation in Metric-Affine Quadratic Gravity
• Teleparallel Spin Connection
• Hamiltonian Analysis of Poincaré Gauge Theory: Higher Spin Modes
• 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
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• General Poincaré gauge theory: Hamiltonian structure and particle spectrum
• Low-energy general relativity with torsion: a systematic derivative expansion
• Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"
• On an integrable geometrical foundation of gravity
• Higgs inflation in Einstein-Cartan gravity
• Ghost and tachyon free Poincaré gauge theories: a systematic approach
• The particle spectrum of parity-violating Poincaré gravitational theory
• Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation
• Weyl vs. Conformal
• Quintessential inflation in Palatini $f(R)$ gravity
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms
• Scale independent $R^2$ inflation
• Torsion and the Electromagnetic Field
• Dark matter as a Weyl geometric effect
• The Raychaudhuri equation in spacetimes with torsion and non-metricity
• Revisiting the Stability of Quadratic Poincaré Gauge Gravity
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Palatini $R^2$ Quintessential Inflation
• Massive Spin-2 fields of Geometric Origin in Curved Spacetimes
• Quantum gravity with torsion and non-metricity
• Einstein-Cartan Portal to Dark Matter
• Cosmological applications of Myrzakulov gravity
• Matter matters in Einstein-Cartan gravity
• A cosmological model in Weyl-Cartan spacetime
• Higgs inflation and teleparallel gravity
• Sterile neutrino dark matter via coinciding resonances
• Infrared Modified Gravity with Dynamical Torsion
• Gravitational waves in Poincaré gauge gravity theory
• Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
• Sub-Planckian ${\varphi }^2$ Inflation in the Palatini Formulation of Gravity with an $R^2$ term
• Poincaré gauge gravity: An overview
• Constant-roll in the Palatini-$R^2$ models
• Minimal coupling in presence of non-metricity and torsion
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Generalized plane waves in Poincaré gauge theory of gravity
• Critical point Higgs inflation in the Palatini formulation
• Cosmological Perturbations in Palatini Formalism
• Weyl gauge theories of gravity do not predict a second clock effect
• Modified gravity: a unified approach to metric-affine models
• On the (non-)uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatini formalism
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• Conformal inflation in the metric-affine geometry
• Remarks on Barbero-Immirzi parameter as a field
• Matter with dilaton charge in Weyl-Cartan spacetime and evolution of the Universe
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• Inflation and Reheating in f(R,h) theory formulated in the Palatini formalism
• The dark side of the torsion: Dark Energy from propagating torsion
• Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories
• Inflation as a spontaneous symmetry breaking of Weyl symmetry
• Electroweak vacuum decay in metric-affine gravity
• The Full Quadratic Metric-Affine Gravity (Including Parity Odd Terms): Exact solutions for the Affine-Connection
• Nonmetricity theories and aspects of gauge symmetry
• Multiple point criticality principle and Coleman-Weinberg inflation
• Weyl Scaling Invariant $R^2$ Gravity for Inflation and Dark Matter
• The Cosmology of Quadratic Torsionful Gravity
• Some Remarks on the Coupling Prescription of Teleparallel Gravity
• One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry
• Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Is the spin connection confined or condensed?
• Compact stellar structures in Weyl geometric gravity
• Non-Riemannian Cosmology: The role of Shear Hypermomentum
• Stability of non-degenerate Ricci-type Palatini theories
• Consistent inflationary cosmology from quadratic gravity with dynamical torsion
• Ghost and tachyon free Weyl gauge theories: a systematic approach
• The Scales of the Infrared
• Extended interactions in the Palatini-$R^2$ inflation
• Cosmic Acceleration with Torsion and Non-metricity in Friedmann-like Universes
• The Timescales of Quantum Breaking
• A metric-affine version of the Horndeski theory
• Describing metric-affine theories anew: alternative frameworks, examples and solutions
• Geometric Proca with Matter in Metric-Palatini Gravity
• Constant-Roll Inflation in modified $f(R,\varphi )$ gravity model using Palatini Formalism
• Late-time acceleration and inflation in a Poincaré gauge cosmological model
• Geometrical Trinity of Unimodular Gravity
• Gravitational corrections to electroweak vacuum decay: metric vs. Palatini
• Planck and Electroweak Scales Emerging from Conformal Gravity
• Path integral measure for first order and metric gravities
• Inflation in the general Poincaré gauge cosmology
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Gravitational four-fermion interaction on the Planck scale
• Conformal Metric-Affine Gravities
• Non-perturbative production of fermionic dark matter from fast preheating
• Gravitational four-fermion interaction and dynamics of the early Universe
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• A Minimal Model of Torsion Mediated Dark Matter
• Sources of torsion in Poincare gauge theory
• Spontaneous scale symmetry breaking at high temperature
• Infinitesimal Gribov copies in gauge-fixed topological Yang-Mills theories

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