Jacobson's thermodynamic approach applied to non-Riemannian geometries selects the Einstein-Hilbert action plus a quadratic torsion term as Nature's choice when non-metricity is absent and the metric energy-momentum tensor is used.
hub
Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
12 Pith papers cite this work. Polarity classification is still indexing.
12
Pith papers citing it
abstract
In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup ${GL}(4,R)$ in four dimensions, energy--momentum and hypermomentum currents of matter are canonically coupled to the one--form basis and to the connection of a metric--affine spacetime with nonvanishing torsion and nonmetricity, respectively. Fermionic matter can be described in this framework by half--integer representations of the $\overline{SL}(4,R)$ covering subgroup. --- We set up a (first--order) Lagrangian formalism and build up the corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive Yang-Mills like form. The conservation--type differential identities for energy--momentum and hypermomentum and the corresponding complexes and superpotentials are derived. Limiting cases such as the Einstein--Cartan theory are discussed. In particular we show, how the ${A}(4,R)$ may ``break down'' to the Poincar\'e (inhomogeneous Lorentz) group. In this context, we present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the ${SL}(4,R)$, or the ${GL}(4,R)$.
hub tools
citation-role summary
background 2
citation-polarity summary
verdicts
UNVERDICTED 12roles
background 2polarities
background 2representative citing papers
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
Derives background-hierarchy bounds on the two free parameters of Type 3 NGR to ensure linear cosmological perturbation theory remains viable around flat FLRW.
In a Thurston-geometry-dependent gravity theory, non-tilted BKS cosmologies admit shear-free perfect-fluid and static vacuum solutions for all topologies, isotropize under positive Lambda except for some Bianchi II cases, and never recollapse when the weak energy condition holds.
A gauge covariant Lie derivative procedure determines co-frame and spin connection ansatzes for symmetric Riemann-Cartan geometries and solves the zero curvature constraint for corresponding metric teleparallel cases, illustrated on spherical, Gödel, de Sitter and other spacetimes.
A naturally light scalar-like distortion field emerges in generalized gravity and mixes with the Higgs boson.
A metric-affine-like generalization of Yang-Mills theory is constructed by making the Hermitian form and connection independent, yielding new fields B_a, h, G_ab, N_a that become massive via GL(n,C) to U(n) breaking and decouple in the infinite-mass limit.
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
A metric-affine-like generalization of Yang-Mills theory adds new interacting fields B_a, h, G_ab and N_a that become massive after spontaneous breaking of GL(n,C) to U(n) and recover standard YM when the mass scale goes to infinity.
Off-diagonal Einstein solutions constructed via the anholonomic frame and connection deformation method can mimic f(R) gravity and dynamical dark energy effects inside GR and Lambda CDM cosmology.
TEGR is argued to admit a gauge theory formulation on principal bundles with Poincaré or Lorentz structure groups, where the gauge group is the diffeomorphism group if the teleparallel connection is not treated as an absolute element.
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
citing papers explorer
-
Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature
Jacobson's thermodynamic approach applied to non-Riemannian geometries selects the Einstein-Hilbert action plus a quadratic torsion term as Nature's choice when non-metricity is absent and the metric energy-momentum tensor is used.
-
Degenerate higher-order scalar-tensor theories in metric-affine gravity
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
-
Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds
Derives background-hierarchy bounds on the two free parameters of Type 3 NGR to ensure linear cosmological perturbation theory remains viable around flat FLRW.
-
Bianchi cosmologies in a Thurston-based theory of gravity
In a Thurston-geometry-dependent gravity theory, non-tilted BKS cosmologies admit shear-free perfect-fluid and static vacuum solutions for all topologies, isotropize under positive Lambda except for some Bianchi II cases, and never recollapse when the weak energy condition holds.
-
Using Gauge Covariant Lie Derivatives in Poincar\'{e} Gauge and Metric Teleparallel Theories of Gravity
A gauge covariant Lie derivative procedure determines co-frame and spin connection ansatzes for symmetric Riemann-Cartan geometries and solves the zero curvature constraint for corresponding metric teleparallel cases, illustrated on spherical, Gödel, de Sitter and other spacetimes.
-
Naturally Light Distortion
A naturally light scalar-like distortion field emerges in generalized gravity and mixes with the Higgs boson.
-
New "metric-affine-like" generalization of Yang-Mills theory
A metric-affine-like generalization of Yang-Mills theory is constructed by making the Hermitian form and connection independent, yielding new fields B_a, h, G_ab, N_a that become massive via GL(n,C) to U(n) breaking and decouple in the infinite-mass limit.
-
Extrinsic geometry and Hamiltonian analysis of symmetric teleparallel gravity
Symmetric teleparallel gravity has the same number of degrees of freedom as general relativity, confirmed via its Hamiltonian formulation after deriving generalized extrinsic geometry relations.
-
"Metric-affine-like" generalization of YM (mal-YM): detailed classical consideration
A metric-affine-like generalization of Yang-Mills theory adds new interacting fields B_a, h, G_ab and N_a that become massive after spontaneous breaking of GL(n,C) to U(n) and recover standard YM when the mass scale goes to infinity.
-
Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology
Off-diagonal Einstein solutions constructed via the anholonomic frame and connection deformation method can mimic f(R) gravity and dynamical dark energy effects inside GR and Lambda CDM cosmology.
-
Teleparallel gravity from the principal bundle viewpoint
TEGR is argued to admit a gauge theory formulation on principal bundles with Poincaré or Lorentz structure groups, where the gauge group is the diffeomorphism group if the teleparallel connection is not treated as an absolute element.
-
The Quintom theory of dark energy after DESI DR2
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.