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Teleparallel axions and cosmology
General Relativity and Quantum Cosmology · Submitted 28 Dec 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity.
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We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. | contribution 0.78 | 0.80 | 0.03 | asserted 0.87 |
| s1 | Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. | method 0.31 | 0.25 | 0.05 | asserted 0.92 |
| s2 | In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. | contribution 0.47 | 0.67 | 0.03 | asserted 0.97 |
| s3 | For the most general coupling of a single axion field, we derive the cosmological field equations. | method 0.58 | 0.96 | 0.05 | asserted 0.97 |
| s4 | We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. | result 1.00 | 0.95 | 0.24 | asserted 1.00 |
| s5 | Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. | result 0.80 | 0.89 | 0.66 | asserted 0.99 |
| s6 | For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. | contribution 0.48 | 0.91 | 0.08 | asserted 0.86 |
| s7 | Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity. | future work 0.98 | 0.65 | 0.03 | hedged possibility 0.62 |
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Original abstract
We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.
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References
How the literature uses it
18 arXiv papers cite this in 26 sentences
Papers citing it · 12 sentences without a confident label
Builds on it 2 papers
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As a generalization of the NYTG model, we will in this paper consider the couplings of $θ(x)$ to both $𝒫_1$ and $𝒫_2$ as in Ref. [ref] .
Ghost instability in the teleparallel gravity model with parity violations · The Parity Violating gravity model as an extension of NYTG model · 0.81
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Further the study of pseudo scalar/axion couplings [ref] will also be extended to spherical symmetry.
Scalarized Black Holes in Teleparallel Gravity · Conclusions · 0.92
Compares with it 1 paper
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The above equations of the background evolutions are consistent with the results of Ref. [ref] , where the tetrad field was parametrized separately as the “vector branch" and “axial branch" {see the Eqs. (29) and (30) in [ref] }, and these two branches match in the case of a spatially-flat universe ($K=0$).
Revisiting a parity violating gravity model without ghost instability: Local Lorentz covariance · Open FRW universe · 0.99
Cites it as background 11 papers
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The polarized GWs have been extensively studied with NY term and its extensions (i.e., the parity violating extension of teleparallel equivalent General Relativity) [ref] , as well as in more general models with non-vanishing torsion and/or nonmetricity tensors [ref] .
Polarized gravitational waves in the parity violating scalar-nonmetricity theory · Introduction · 0.84
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In particular, teleparallel gravity, which is with non-metricity tensor $Q_ρμν = ∇_ρ g_μν$ and/or torsion, were proposed and attracted much attention [ref] .
Scalar induced gravitational waves in symmetric teleparallel gravity with a parity-violating term · Introduction · 0.97
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Most of the previous works discussing torsional instantons or the Nieh-Yan term were conducted either in this context [ref] , or various axion-like modified gravity theories [ref] .
Self-Excited Gravitational Instantons · Discussion and Conclusions · 0.91
What it cites · 45 sentences without a confident label
Builds on 9 papers
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In this article, we generalize the theory presented in [ref] and construct the most general quadratic teleparallel theory of gravity employing all five quadratic torsion scalar terms.
A simple parity violating gravity model without ghost instability · Introduction · 1.00
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In this article, we generalize the theory presented in [ref] and construct the most general quadratic teleparallel theory of gravity employing all five quadratic torsion scalar terms.
Torsion-induced gravitational $\theta$ term and gravitoelectromagnetism · Introduction · 1.00
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A possible action one can conceive in analogy to the teleparallel axion model [ref] as generalization of newer general relativity [ref] is then given by [equation] In the case that the parameters take the values [equation] one obtains the symmetric teleparallel equivalent of relativity [ref] (STEGR), together with symmetric teleparallel axion, which is non-minimally coupled to the unique parity-odd invariant of non-metricity.
Coincident General Relativity · Symmetric teleparallel axions · 0.96
Uses the method or tool of 1 paper
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The most straightforward is to apply the method of dynamical systems [ref] and study the axion contribution in the light of inflation.
Dynamical systems applied to cosmology: dark energy and modified gravity · Conclusion · 0.92
Cites as support 2 papers
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However, this will not restrict the following analysis, in which we investigate these equations in cosmological symmetry, since any antisymmetric two-tensor with cosmological symmetry vanishes identically, as shown in [ref] , and therefore does not contribute to the cosmological dynamics.
Modified teleparallel theories of gravity in symmetric spacetimes · Field equations · 0.97
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Further assuming that the matter action is invariant under local Lorentz transformations, we find that the energy-momentum tensor must be symmetric [ref] , hence \(Θ_[μν] = 0\).
Teleparallel theories of gravity as analogue of non-linear electrodynamics · The Action · 0.97
Cites as background 12 papers
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These are the Holst term [ref] [equation] and the topological Nieh-Yan term [ref] [equation] Note that the Riemann tensor obtained from the Levi-Civita connection does not appear in these terms, since its totally antisymmetric part vanishes as a consequence of the first Bianchi identity; hence, no such parity violating terms may be constructed in Riemannian geometry, where the torsion tensor vanishes.
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action · Special cases and related theories · 0.91
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The fundamental field variables in the covariant formulation of teleparallel gravity are the tetrad \(θ^a_μ\) and a flat Lorentz spin connection \(ω^a_bμ\) [ref] .
The covariant formulation of f(T) gravity · The general setting · 0.99
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Besides the most well-known formulation of general relativity in terms of curvature, alternative formulations based on torsion or nonmetricity have been conceived [ref] , giving rise to the so called symmetric teleparallel equivalent of general relativity (STEGR) [ref] and the teleparallel equivalent of general relativity (TEGR) [ref] .
Symmetric teleparallel general relativity · Introduction · 0.99
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