Pith. sign in

REVIEW 3 major objections 5 minor 72 references

$f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read In f(T) gravity, the gravity sector carries exactly two propagating degrees of freedom—the two gravitational-wave polarizations—on both FLRW and Bianchi I backgrounds, with no extra scalar mode at linear order.

desk verdict A serious, readable contribution to the f(T) degree-of-freedom debate: the FLRW part redoes known results, the Bianchi I part is genuinely new, and the two-mode conclusion is plausible but rests on a gauge choice and algebraic eliminations that are not fully justified. read the letter →

arxiv 2502.07890 v2 pith:KYEMRXAY submitted 2025-02-11 gr-qc astro-ph.CO

Valentina Danieli , Antonio De Felice This is my paper · ORCID
classification gr-qcastro-ph.CO PACS 04.50.Kd98.80.-k
keywords f(T)gravityteleparallelpropagatingdegreesoffreedomFLRWspacetimeBianchiILorentztransformationsgravitational-wavepolarizationsno-ghostcondition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to settle a long-running dispute over how many degrees of freedom f(T) gravity actually carries. By expanding the vierbein action to second order in perturbations around a flat FLRW spacetime and an anisotropic Bianchi I spacetime, the authors claim that the gravity sector contains exactly two propagating fields, the two polarizations of gravitational waves, and that no extra scalar mode appears. The same conclusion holds even when the background Lorentz (spin-connection) degrees of freedom are allowed to vary: on FLRW they are forced to be constant and drop out, while on Bianchi I a two-function family of background Lorentz transformations exists but leaves both the background dynamics and the propagating perturbations unaffected. The finding matters because it would mean f(T) gravity does not inherit the extra scalar degree of freedom that f(R) gravity acquires, strengthening its case as a viable modified-gravity alternative. The authors themselves caution that the result is not definitive, since a strongly coupled extra mode could hide at linear order.

What carries the argument

The machinery is the second-order perturbation of the vierbein action, written in ADM variables with an explicit background Lorentz matrix $\bar{\Lambda}$ built from three boosts with rapidities $\eta_i$ and three rotations with angles $\theta_i$. The torsion scalar $T$ depends only on first derivatives of the Lorentz-transformed vierbein, so the quadratic action yields at most second-order equations of motion and the field content can be read off by identifying which fields carry time derivatives. The equations of motion are then solved order by order: algebraic equations eliminate Lagrange multipliers such as $n^V_m$, $\varphi$, $n_1$, and $\zeta_1$, while the surviving fields $w^V_m$ (odd mode) and $d_1$ (even mode) carry the dynamics; the reduced Lagrangian in Fourier space fixes the no-ghost condition $f_{,T} > 0$ and the dispersion relation $\omega^2 = K^2 + Q^2$. A spatially flat gauge is imposed on each background, and the same gauge choices reduce to each other in the isotropic limit.

What would settle it

Compute the principal symbol of the full non-linear f(T) field equations on a Bianchi I background and look for more than two characteristic modes, or take the same second-order action to cubic order and check whether any field eliminated as a Lagrange multiplier (for example $s_2$ or the combination of $\zeta_1$, $\zeta_2$, $\zeta^V_m$, $s_2$) acquires a kinetic term; either result would show that the two-mode count is an artifact of the linear truncation or of the gauge choice.

Watch

Extended reading notes

Core claim

On a flat FLRW background, the second-order perturbation action yields three propagating fields in total—the matter density perturbation and the two tensor polarizations—with the tensor modes obeying the no-ghost condition $f_{,T} > 0$ and propagating at the speed of light; all other scalar and vector perturbations are Lagrange multipliers fixed by algebraic equations. On a vacuum Bianchi I background with constant torsion scalar $T = T_0$ and $T_0 > 0$, the same perturbative treatment reduces the gravity sector to two propagating modes, an even mode $d_1$ and an odd mode $w^V_m$, with dispersion relation $\omega^2 = K^2 + Q^2$, implying luminal propagation, and no-ghost condition $f_{,T} > 0$. The remaining fields are eliminated algebraically or drop out entirely, including the Lorentz-transformation variables $\eta_i(t)$ and $\theta_i(t)$, which appear only in the relations among Lagrange multipliers. The paper's central conclusion is that, at linear order, f(T) gravity possesses no extra scalar degree of freedom on either background, so the gravity sector on Bianchi I carries the same two gravitational-wave polarizations as on FLRW.

Load-bearing premise

The load-bearing premise is that a quadratic perturbation expansion around FLRW and Bianchi I spacetimes captures every dynamical degree of freedom, so that fields eliminated by algebraic equations at linear order are truly non-dynamical.

Editorial extensions

If this is right

  • If the central claim is right, f(T) gravity does not acquire the extra scalar degree of freedom that f(R) gravity acquires, so late-time acceleration would have to be explained by the modified background dynamics rather than by a new scalar field.
  • Gravitational waves in f(T) gravity travel at the speed of light in the sub-horizon regime on both backgrounds, and the no-ghost condition $f_{,T} > 0$ doubles as the condition for a positive effective Newton constant, $G_{\rm eff}/G_N = 1/f_{,T}$.
  • On a Bianchi I vacuum background the two polarizations are the only gravity-sector modes; all vector and scalar perturbation variables are either Lagrange multipliers or undetermined gauge-like combinations, and the Lorentz functions $\eta_i$ and $\theta_i$ do not enter the propagating equations.
  • The Bianchi I vacuum solutions with $T_0 > 0$ isotropize to a de Sitter spacetime at late times, so the two-mode conclusion applies on the background that dynamically approaches FLRW, while solutions with $T_0 < 0$ contain curvature and torsion singularities.
  • The paper's own caveat is that the two-mode count is not definitive: the absence of extra modes at linear order could signal a strong-coupling problem, and the question of the true degree-of-freedom count remains open.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the two-mode count survives on more general backgrounds, the apparent disagreement with Hamiltonian counts of three or five degrees of freedom would most likely be resolved by strong coupling: a would-be scalar mode that becomes dynamical only at higher orders in perturbation theory, a possibility the authors leave open.
  • The two-function family of background Lorentz transformations on Bianchi I may be interpreted as a redundancy of the vierbein formulation rather than physical new solutions, since it leaves both the background scalar $T$ and the propagating mode equations unchanged; this could simplify the covariant spin-connection formulation.
  • A direct test of the paper's conclusion would be to push the Bianchi I expansion to cubic order or to compute the principal symbol of the full non-linear field equations; if an extra characteristic mode appears, the linear count is an artifact of the gauge choice or the quadratic truncation.
  • Observationally, if future gravitational-wave standard sirens measure a departure of the tensor speed from $c$ in a regime where $f_{,T} > 0$, the claim of luminal propagation on these backgrounds would be falsified; conversely, the absence of such a departure is consistent with this analysis.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper analyzes the role of background Lorentz transformations in f(T) teleparallel gravity and studies the linearized propagating degrees of freedom on flat FLRW and Bianchi I spacetimes. On FLRW the background Lorentz matrix is shown to be constant and reducible to the identity; on a vacuum Bianchi I background a two-function family of Lorentz matrices survives but does not affect the background torsion scalar or the Friedmann equations. Expanding the action to second order in perturbations, the authors find, in the spatially-flat gauge, three propagating modes on FLRW with a perfect fluid (the matter density perturbation and two gravitational-wave polarizations) and, on vacuum Bianchi I, only two propagating gravity-sector modes: an even scalar d1 and an odd vector w_V^m, both luminal in the sub-horizon limit and subject to the no-ghost condition f_T>0. The reduction on Bianchi I is performed by algebraic elimination of auxiliary fields, reported in Appendix A.

Significance. If fully established, the Bianchi I result would support the claim that f(T) gravity has no extra scalar degree of freedom on homogeneous cosmological backgrounds, in contrast with several Hamiltonian analyses. The paper's strengths are its explicit exact background solutions (4.31)-(4.39), the closed-form reduced Lagrangian (4.46), and an honest discussion of the limits of the linear analysis. The FLRW part is well supported and consistent with the literature. The Bianchi I two-mode count, however, is not yet proven for the full family of allowed backgrounds: the algebraic elimination of ζ1 degenerates when cosh(2η_z)+cos(2θ_z)=0, and the spatially-flat gauge is imposed without an admissibility proof. These are load-bearing points for the central claim, so the result should be treated as conditional until they are resolved.

major comments (3)
  1. [§IV.B.2, Eq. (A2)] The algebraic solution for ζ1 (Eq. A2) divides by the factor [cosh(2η_z)+cos(2θ_z)]. The background Lorentz parameters η_z and θ_z are free functions not fixed by the background equations (Section IV.A), and real, allowed values such as η_z=0, θ_z=π/2 make this factor vanish. At those points the equation of motion for ζ1 does not determine ζ1, so the elimination of ζ1 as a Lagrange multiplier is invalid on a subfamily of the allowed anisotropic backgrounds. The two-mode count is therefore established only where the denominator is nonzero, and the conclusion that the Lorentz functions never affect the propagating sector is not established for the full Bianchi I family. This needs either a separate treatment of the degenerate points or a restriction of the claim.
  2. [§IV.B.2, Eq. (4.40)] The spatially-flat gauge is imposed on the Bianchi I background without proving that it is reachable by a linearized diffeomorphism. In the FLRW case the authors note that this gauge is allowed only if H≠0 (footnote 12); an analogous condition for the anisotropic 1+1+2 background is absent. If the conditions d2=0, ψ=0, E=0, C_V^m=0 cannot be imposed simultaneously without freezing a dynamical combination of the metric and Lorentz perturbations, the count of two propagating modes is incomplete. Please provide the gauge-fixing argument or verify the conditions against the linearized diffeomorphism transformations.
  3. [Appendix A] The full second-order action on Bianchi I is not displayed; only the final equations of motion (A1)-(A4) and the reduced Lagrangian (4.46) are given. Because the claim is precisely that all fields eliminated via these algebraic relations have no kinetic terms, the reader needs to check that the quadratic action contains no hidden time derivatives of ζ1, ζ2, ζ_V^m, s2, n1, n2, or φ after integration by parts on the time-dependent anisotropic background. Without the quadratic action, the Lagrange-multiplier identification is asserted rather than demonstrated. Presenting the second-order action (or at least the kinetic matrix) would make the count verifiable.
minor comments (5)
  1. [§V] The sentence "the speed of propagation of the two polarizations is the speed of light also on a Bianchi I background, as it can be seen in (2.8)" cites Eq. (2.8), which defines the spin connection; the correct references are Eqs. (4.43)-(4.44) and (4.46).
  2. [§III.B.2, Eq. (3.34)] The denominator "2M_Pl f_T" should be "2M_Pl^2 f_T" to be consistent with the Planck-mass normalization used in the action (2.11).
  3. [Abstract] The phrase "only two fields propagate in the gravity sector" should be qualified as a statement about linear perturbation theory around the specified backgrounds; the conclusion already correctly notes that the question of a strongly coupled mode remains open.
  4. [§II, Eq. (2.13)] There is an index mismatch in Eq. (2.13): the right-hand side contains e^c_µ while the left-hand side is eAν; the index should be ν.
  5. [§IV.B.2, Eq. (4.46)] The notation (w_V^m)^2 = w_V^m(t,-k,-q) w_V^m(t,k,q) is ambiguous; using an explicit complex-conjugate or mode-product notation would be clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the two-mode result is derived by explicit perturbative reduction of the action, not by fitting or self-referential definitions.

full rationale

The paper's central claim that only two gravity-sector fields propagate on FLRW and Bianchi I backgrounds is obtained by a direct second-order expansion of the f(T) action around explicitly written backgrounds, followed by gauge fixing and algebraic elimination of Lagrange-multiplier fields. The key steps are displayed in the text: the spatially flat gauge choices (3.22) and (4.40), the algebraic solutions (A1)-(A4), and the reduced Lagrangian (4.46) containing kinetic terms for only wV_m and d1. No parameter is fitted to force the two-mode conclusion, and the propagating fields are not defined in terms of the result they are supposed to establish. Self-citations appear only as standard background references, such as [14] for the f(R) expectation of an extra scalar degree of freedom, and they are not load-bearing for the Bianchi I calculation. The paper's own caveat that a strongly coupled extra mode could evade linear analysis, and the possible degeneracy of the denominator in (A2), are robustness or correctness concerns rather than circularity, because the derivation does not reduce to its inputs or to prior claims imported from the authors. The analysis is therefore self-contained for the purposes of circularity assessment, and the appropriate score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard f(T) action, symmetry-based reduction of the background Lorentz matrix, and the perturbative criterion that algebraic fields are non-propagating. No numerical free parameters are fitted to data; the Bianchi I family contains two undetermined background functions eta_x and theta_x, but the paper shows these do not enter the propagating equations. The strongest extra assumption is that strong coupling does not hide additional degrees of freedom at linear order.

assumptions (5)
  • domain assumption The action S = -M_Pl^2/2 integral e f(T), with T built from the Weitzenbock connection, is the correct starting point for f(T) gravity.
    Adopted in Eq. (2.11); all background and perturbation equations follow from this action.
  • domain assumption A homogeneous Bianchi I background with isotropy in the (y,z) plane admits a proper orthochronous background Lorentz matrix of the product form (2.22) with six time-dependent functions.
    Used in Section IV.A to reduce background torsion constraints and leave two free functions, eta_x and theta_x.
  • domain assumption The spatially flat gauge (4.40) is admissible on Bianchi I and does not remove a propagating mode.
    This gauge is imposed before solving the equations of motion; its validity on an anisotropic background is asserted rather than proven.
  • domain assumption A field that can be eliminated by an algebraic equation of motion at quadratic order is a Lagrange multiplier and carries no propagating degree of freedom.
    The degree-of-freedom count relies on this standard perturbative criterion, applied to nV_m, n1, n2, phi, zeta1, and related fields in Section IV.B.2 and Appendix A.
  • domain assumption No strongly coupled extra degree of freedom exists below the cutoff of the linear analysis.
    The authors explicitly state that the absence of extra modes in perturbation theory may signal strong coupling, citing references [66] through [68].

how reviews work

0 comments
Cite this review

Pith. "Pith review of $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom." pith.science (2026). https://pith.science/paper/KYEMRXAY

@misc{pith2026250207890,
  author       = {Pith},
  title        = {Pith review of: $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KYEMRXAY}},
  note         = {Machine review of arXiv:2502.07890}
}
abstract

The standard cosmological model, rooted in General Relativity (GR), has achieved remarkable success, yet it still faces unresolved issues like the nature of dark matter, dark energy, and the Hubble tension. These challenges might imply the need for alternative gravitational theories. Teleparallel gravity offers a compelling framework by reformulating the gravitational interaction using torsion, rather than curvature, as its fundamental geometrical property. This paper delves into $f(T)$ gravity, an extension of the Teleparallel Equivalent of General Relativity (TEGR), which introduces non-linear modifications of the torsion scalar $T$. We focus on the role of spacetime-dependent Lorentz transformations in the vierbein formalism, examining their impact on both background solutions and perturbation dynamics. Special attention is given to the homogeneous and isotropic FLRW spacetime, as well as the anisotropic Bianchi I spacetime. Furthermore, the analysis of the propagating degrees of freedom on these spacetimes is performed. While it is well established that TEGR reproduces the same results as GR, the propagating degrees of freedom in its non-linear extension, $f(T)$ gravity, is still debated in the literature. In this work, we find that only two fields propagate in the gravity sector, independently of the background spacetime considered, either FLRW or Bianchi I. Although not definitive, this paper provides fresh insights into the issue of the propagating degrees of freedom in $f(T)$ gravity, opening the door to intriguing new directions for further investigation.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 26 canonical work pages

  1. [1]

    The Background Equations of Motion Although the equations for the background variables have been alr eady derived in the literature, we report them here for completeness. On a flat FLR W spacetime, the background torsion scalar reduces to ¯T (t) = 6H 2, (3.14) providing a useful relation between the background torsion scalar and the Hubble factor H(t) = ˙a...

    work page

  2. [2]

    To simplify the calculations we choose a specific gaug e, the spatially flat gauge

    Propagating Degrees of Freedom Having the action in terms of background and perturbation variable s, we can expand it up to second order in the perturbations. To simplify the calculations we choose a specific gaug e, the spatially flat gauge. 12 It corresponds to selecting spatial hypersurfaces on which the induced three-dimen sional metric is left unpertur...

    work page

  3. [3]

    This expression simplifies to 6 H 2 in the homogeneous and isotropic limit, as expected

    The Background Equations of Motion On a Bianchi I spacetime, the background torsion tensor reduces to: ¯T (t) = 4HL + 2L2, (4.24) where we have introduced two Hubble factors H = ˙a/a and L = ˙b/b. This expression simplifies to 6 H 2 in the homogeneous and isotropic limit, as expected. It should be noted th at ¯T does not depend on ηi or θi, although the an...

    work page

  4. [4]

    From the action expanded up to the second order in Fourier space, we can co mpute the equations of motion

    Propagating Degrees of Freedom Having solved the equations for the background, we now proceed t o analyze the perturbations dynamics. From the action expanded up to the second order in Fourier space, we can co mpute the equations of motion. To simplify the computations we set again the spatially flat gauge, which now corres ponds to: CV m = 0, d 2 = 0, ψ =...

    work page

  5. [5]

    Asmodelle, Tests of General Relativity: A Review , bachelor thesis, Central Lancashire U., 2017, [ 1705.04397]

    E. Asmodelle, Tests of General Relativity: A Review , bachelor thesis, Central Lancashire U., 2017, [ 1705.04397]

    arXiv 2017

  6. [6]

    Bertone, D

    G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and constraint s, Phys. Rept. 405 (2005) 279 [ hep-ph/0404175]

    arXiv 2005

  7. [7]

    Arbey and F

    A. Arbey and F. Mahmoudi, Dark matter and the early Universe: a review , Prog. Part. Nucl. Phys. 119 (2021) 103865 [2104.11488]

    arXiv 2021

  8. [8]

    Li, X.-D

    M. Li, X.-D. Li, S. Wang and Y. Wang, Dark Energy: A Brief Review , Front. Phys. (Beijing) 8 (2013) 828 [ 1209.0922]

    arXiv 2013

Show all 72 references
  1. [9]

    Hu and F.-Y

    J.-P. Hu and F.-Y. Wang, Hubble Tension: The Evidence of New Physics , Universe 9 (2023) 94 [ 2302.05709]

    2023 arXiv

  2. [10]

    An Update by the CANTATA Netw ork, Springer (2021), 10.1007/978-3-030-83715-0, [ 2105.12582]

    CANTATAcollaboration, Modified Gravity and Cosmology. An Update by the CANTATA Netw ork, Springer (2021), 10.1007/978-3-030-83715-0, [ 2105.12582]

    2021 arXiv

  3. [11]

    Beltr´ an Jim´ enez, L

    J. Beltr´ an Jim´ enez, L. Heisenberg and T.S. Koivisto, The Geometrical Trinity of Gravity , Universe 5 (2019) 173 [1903.06830]

    2019 arXiv

  4. [12]

    Heisenberg, A systematic approach to generalisations of General Relati vity and their cosmological implications , Phys

    L. Heisenberg, A systematic approach to generalisations of General Relati vity and their cosmological implications , Phys. Rept. 796 (2019) 1 [ 1807.01725]

    2019 arXiv

  5. [13]

    Capozziello, V

    S. Capozziello, V. De Falco and C. Ferrara, Comparing equivalent gravities: common features and differe nces, Eur. Phys. J. C 82 (2022) 865 [ 2208.03011]

    2022 arXiv

  6. [14]

    Aldrovandi and J.G

    R. Aldrovandi and J.G. Pereira, Teleparallel Gravity: An Introduction , Springer (2013), 10.1007/978-94-007-5143-9

    2013 doi

  7. [15]

    Maluf, The teleparallel equivalent of general relativity , Annalen Phys

    J.W. Maluf, The teleparallel equivalent of general relativity , Annalen Phys. 525 (2013) 339 [ 1303.3897]

    2013 arXiv

  8. [16]

    Nester and H.-J

    J.M. Nester and H.-J. Yo, Symmetric teleparallel general relativity , Chin. J. Phys. 37 (1999) 113 [ gr-qc/9809049]

    1999 arXiv

  9. [17]

    Sotiriou and V

    T.P. Sotiriou and V. Faraoni, f(R) Theories Of Gravity , Rev. Mod. Phys. 82 (2010) 451 [ 0805.1726]

    2010 arXiv

  10. [18]

    De Felice and S

    A. De Felice and S. Tsujikawa, f(R) theories , Living Rev. Rel. 13 (2010) 3 [ 1002.4928]

    2010 arXiv

  11. [19]

    Hohmann, Teleparallel Gravity, Lect

    M. Hohmann, Teleparallel Gravity, Lect. Notes Phys. 1017 (2023) 145 [ 2207.06438]

    2023 arXiv

  12. [20]

    Wu and H.W

    P. Wu and H.W. Yu, Observational constraints on f (T ) theory, Phys. Lett. B 693 (2010) 415 [ 1006.0674]

    2010 arXiv

  13. [21]

    X. Fu, P. Wu and H. Yu, The growth of matter perturbations in f(T) gravity , Int. J. Mod. Phys. D 20 (2011) 1301 [1204.2333]

    2011 arXiv

  14. [22]

    Bahamonde, K.F

    S. Bahamonde, K.F. Dialektopoulos, C. Escamilla-Rive ra, G. Farrugia, V. Gakis, M. Hendry et al., Teleparallel gravity: from theory to cosmology , Rept. Prog. Phys. 86 (2023) 026901 [ 2106.13793]

    2023 arXiv

  15. [23]

    Cardone, N

    V.F. Cardone, N. Radicella and S. Camera, Accelerating f(T) gravity models constrained by recent cos mological data, Phys. Rev. D 85 (2012) 124007 [ 1204.5294]

    2012 arXiv

  16. [24]

    Farrugia, J

    G. Farrugia, J. Levi Said and M.L. Ruggiero, Solar System tests in f(T) gravity , Phys. Rev. D 93 (2016) 104034 [1605.07614]

    2016 arXiv

  17. [25]

    Z. Chen, W. Luo, Y.-F. Cai and E.N. Saridakis, New test on general relativity and f (T ) torsional gravity from galaxy-galaxy weak lensing surveys , Phys. Rev. D 102 (2020) 104044 [ 1907.12225]. 18

    2020 arXiv

  18. [26]

    Golovnev and M.-J

    A. Golovnev and M.-J. Guzm´ an, Bianchi identities in f (T ) gravity: Paving the way to confrontation with astrophysics , Phys. Lett. B 810 (2020) 135806 [ 2006.08507]

    2020 arXiv

  19. [27]

    X. Ren, Y. Zhao, E.N. Saridakis and Y.-F. Cai, Deflection angle and lensing signature of covariant f(T) gra vity, JCAP 10 (2021) 062 [ 2105.04578]

    2021 arXiv

  20. [28]

    Ren, T.H.T

    X. Ren, T.H.T. Wong, Y.-F. Cai and E.N. Saridakis, Data-driven Reconstruction of the Late-time Cosmic Accele ration with f(T) Gravity , Phys. Dark Univ. 32 (2021) 100812 [ 2103.01260]

    2021 arXiv

  21. [29]

    Golovnev and M.-J

    A. Golovnev and M.-J. Guzm´ an, Approaches to spherically symmetric solutions in f(T) grav ity, Universe 7 (2021) 121 [2103.16970]

    2021 arXiv

  22. [30]

    DeBenedictis, S

    A. DeBenedictis, S. Iliji´ c and M. Sossich, Spherically symmetric vacuum solutions and horizons in cov ariant f(T) gravity theory, Phys. Rev. D 105 (2022) 084020 [ 2202.08958]

    2022 arXiv

  23. [31]

    Y. Zhao, X. Ren, A. Ilyas, E.N. Saridakis and Y.-F. Cai, Quasinormal modes of black holes in f(T) gravity , JCAP 10 (2022) 087 [ 2204.11169]

    2022 arXiv

  24. [32]

    Beltr´ an Jim´ enez and T.S

    J. Beltr´ an Jim´ enez and T.S. Koivisto,Noether charges in the geometrical trinity of gravity , Phys. Rev. D 105 (2022) L021502 [ 2111.04716]

    2022 arXiv

  25. [33]

    Duchaniya, S.V

    L.K. Duchaniya, S.V. Lohakare, B. Mishra and S.K. Tripa thy, Dynamical stability analysis of accelerating f(T) gravity models, Eur. Phys. J. C 82 (2022) 448 [ 2202.08150]

    2022 arXiv

  26. [34]

    Aljaf, E

    M. Aljaf, E. Elizalde, M. Khurshudyan, K. Myrzakulov an d A. Zhadyranova, Solving the H0 tension in f(T) gravity through Bayesian machine learning , Eur. Phys. J. C 82 (2022) 1130 [ 2205.06252]

    2022 arXiv

  27. [35]

    Huang, J

    Y. Huang, J. Zhang, X. Ren, E.N. Saridakis and Y.-F. Cai, N-body simulations, halo mass functions, and halo density profile in f(T) gravity , Phys. Rev. D 106 (2022) 064047 [ 2204.06845]

    2022 arXiv

  28. [36]

    dos Santos, J.E

    F.B.M. dos Santos, J.E. Gonzalez and R. Silva, Observational constraints on f(T) gravity from model-inde pendent data , Eur. Phys. J. C 82 (2022) 823 [ 2112.15249]

    2022 arXiv

  29. [37]

    Myrzakulov, F(T) gravity and k-essence , Gen

    R. Myrzakulov, F(T) gravity and k-essence , Gen. Rel. Grav. 44 (2012) 3059 [ 1008.4486]

    2012 arXiv

  30. [38]

    Wang, Static Solutions with Spherical Symmetry in f(T) Theories , Phys

    T. Wang, Static Solutions with Spherical Symmetry in f(T) Theories , Phys. Rev. D 84 (2011) 024042 [ 1102.4410]

    2011 arXiv

  31. [39]

    Deliduman and B

    C. Deliduman and B. Yapiskan, Absence of Relativistic Stars in f(T) Gravity , 1103.2225

    arXiv

  32. [40]

    Arcos and J.G

    H.I. Arcos and J.G. Pereira, Torsion gravity: A Reappraisal , Int. J. Mod. Phys. D 13 (2004) 2193 [ gr-qc/0501017]

    2004 arXiv

  33. [41]

    Souza, A.M

    M.S. Souza, A.M. Barcelos, R.C. Nunes, O. Akarsu and S. K umar, Mapping the Λ sCDM Scenario to f(T) Modified Gravity: Effects on Structure Growth Rate , Universe 11 (2025) 2 [ 2501.18031]

    2025 arXiv

  34. [42]

    Akarsu, B

    O. Akarsu, B. Bulduk, A. De Felice, N. Katırcı and N.M. Uz un, Unexplored regions in teleparallel f (T ) gravity: Sign-changing dark energy density , 2410.23068

  35. [43]

    Ferraro and F

    R. Ferraro and F. Fiorini, Modified teleparallel gravity: Inflation without inflaton , Phys. Rev. D 75 (2007) 084031 [gr-qc/0610067]

    2007 arXiv

  36. [44]

    Ferraro and F

    R. Ferraro and F. Fiorini, On Born-Infeld Gravity in Weitzenbock spacetime , Phys. Rev. D 78 (2008) 124019 [ 0812.1981]

    2008 arXiv

  37. [45]

    A. Awad, W. El Hanafy, G.G.L. Nashed and E.N. Saridakis, Phase Portraits of general f(T) Cosmology , JCAP 02 (2018) 052 [ 1710.10194]

    2018 arXiv

  38. [46]

    Hashim, W

    M. Hashim, W. El Hanafy, A. Golovnev and A.A. El-Zant, Toward a concordance teleparallel cosmology. Part I. Background dynamics , JCAP 07 (2021) 052 [ 2010.14964]

    2021 arXiv

  39. [47]

    Hashim, A.A

    M. Hashim, A.A. El-Zant, W. El Hanafy and A. Golovnev, Toward a concordance teleparallel cosmology. Part II. Line ar perturbation, JCAP 07 (2021) 053 [ 2104.08311]

    2021 arXiv

  40. [48]

    B. Li, T.P. Sotiriou and J.D. Barrow, f (T ) gravity and local Lorentz invariance , Phys. Rev. D 83 (2011) 064035 [1010.1041]

    2011 arXiv

  41. [49]

    Sotiriou, B

    T.P. Sotiriou, B. Li and J.D. Barrow, Generalizations of teleparallel gravity and local Lorentz symmetry, Phys. Rev. D 83 (2011) 104030 [ 1012.4039]

    2011 arXiv

  42. [50]

    Teyssandier and P

    P. Teyssandier and P. Tourrenc, The Cauchy problem for the R+R**2 theories of gravity withou t torsion , J. Math. Phys. 24 (1983) 2793

    1983

  43. [51]

    D ´ ıaz, D

    B. D ´ ıaz, D. Higuita and M. Montesinos, Lagrangian approach to the physical degree of freedom count , J. Math. Phys. 55 (2014) 122901 [ 1406.1156]

    2014 arXiv

  44. [52]

    Diaz and M

    B. Diaz and M. Montesinos, Geometric Lagrangian approach to the physical degree of fre edom count in field theory , J. Math. Phys. 59 (2018) 052901 [ 1710.01371]

    2018 arXiv

  45. [53]

    Ferraro and M.J

    R. Ferraro and M.J. Guzm´ an, Pseudoinvariance and the extra degree of freedom in f(T) gra vity, Phys. Rev. D 101 (2020) 084017 [ 2001.08137]

    2020 arXiv

  46. [54]

    Gonzalez Quaglia and I

    R. Gonzalez Quaglia and I. Quiros, Local scale symmetry in non-riemannian geometry based grav itational theories and the role of the noether current , Phys. Rev. D 108 (2023) 124058 [ 2309.01845]

    2023 arXiv

  47. [55]

    Li, R.-X

    M. Li, R.-X. Miao and Y.-G. Miao, Degrees of freedom of f (T ) gravity, JHEP 07 (2011) 108 [ 1105.5934]

    2011 arXiv

  48. [56]

    Ferraro and M.J

    R. Ferraro and M.J. Guzm´ an, Quest for the extra degree of freedom in f (T ) gravity, Phys. Rev. D 98 (2018) 124037 [1810.07171]

    2018 arXiv

  49. [57]

    Guzm´ an and R

    M.J. Guzm´ an and R. Ferraro, Degrees of freedom and local Lorentz invariance in f (T) grav ity, in 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experime ntal General Relativity, Astrophysics, and Relativistic F ield Theories, 3, 2019, DOI [ 1903.06774]

    2019 arXiv

  50. [58]

    Blagojevi´ c and J.M

    M. Blagojevi´ c and J.M. Nester, Local symmetries and physical degrees of freedom in f (T ) gravity: a Dirac Hamiltonian constraint analysis, Phys. Rev. D 102 (2020) 064025 [ 2006.15303]

    2020 arXiv

  51. [59]

    J.B. Dent, S. Dutta and E.N. Saridakis, f(T) gravity mimicking dynamical dark energy. Background a nd perturbation analysis, JCAP 01 (2011) 009 [ 1010.2215]

    2011 arXiv

  52. [60]

    Chen, J.B

    S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Cosmological perturbations in f(T) gravity , 19 Phys. Rev. D 83 (2011) 023508 [ 1008.1250]

    2011 arXiv

  53. [61]

    Izumi and Y.C

    K. Izumi and Y.C. Ong, Cosmological Perturbation in f(T) Gravity Revisited , JCAP 06 (2013) 029 [ 1212.5774]

    2013 arXiv

  54. [62]

    B. Li, T.P. Sotiriou and J.D. Barrow, Large-scale Structure in f(T) Gravity , Phys. Rev. D 83 (2011) 104017 [ 1103.2786]

    2011 arXiv

  55. [63]

    Golovnev and T

    A. Golovnev and T. Koivisto, Cosmological perturbations in modified teleparallel gravi ty models , JCAP 11 (2018) 012 [1808.05565]

    2018 arXiv

  56. [64]

    Sahlu, J

    S. Sahlu, J. Ntahompagaze, A. Abebe, A. de la Cruz-Dombr iz and D.F. Mota, Scalar perturbations in f (T ) gravity using the 1 + 3 covariant approach, Eur. Phys. J. C 80 (2020) 422 [ 1907.03563]

    2020 arXiv

  57. [65]

    Bahamonde, K.F

    S. Bahamonde, K.F. Dialektopoulos, M. Hohmann, J. Levi Said, C. Pfeifer and E.N. Saridakis, Perturbations in non-flat cosmology for f(T) gravity , Eur. Phys. J. C 83 (2023) 193 [ 2203.00619]

    2023 arXiv

  58. [66]

    Hohmann, General cosmological perturbations in teleparallel gravi ty, Eur

    M. Hohmann, General cosmological perturbations in teleparallel gravi ty, Eur. Phys. J. Plus 136 (2021) 65 [ 2011.02491]

    2021 arXiv

  59. [67]

    Chiba, N

    T. Chiba, N. Sugiyama and T. Nakamura, Cosmology with x matter , Mon. Not. Roy. Astron. Soc. 289 (1997) L5 [astro-ph/9704199]

    1997 arXiv

  60. [68]

    Armendariz-Picon, V.F

    C. Armendariz-Picon, V.F. Mukhanov and P.J. Steinhard t, Essentials of k essence , Phys. Rev. D 63 (2001) 103510 [astro-ph/0006373]

    2001 arXiv

  61. [69]

    Faraji, Z

    A. Faraji, Z. Molaee and A. Shirzad, Generators of Local Lorentz Transformation in ADM-Vielbei n Formalism of Gravitational Relativity, 2412.00128

    arXiv

  62. [70]

    Bueno and P.A

    P. Bueno and P.A. Cano, Einsteinian cubic gravity , Phys. Rev. D 94 (2016) 104005 [ 1607.06463]

    2016 arXiv

  63. [71]

    Beltr´ an Jim´ enez and A

    J. Beltr´ an Jim´ enez and A. Jim´ enez-Cano,On the strong coupling of Einsteinian Cubic Gravity and its g eneralisations, JCAP 01 (2021) 069 [ 2009.08197]

    2021 arXiv

  64. [72]

    Y.-M. Hu, Y. Zhao, X. Ren, B. Wang, E.N. Saridakis and Y.- F. Cai, The effective field theory approach to the strong coupling issue in f(T) gravity , JCAP 07 (2023) 060 [ 2302.03545]

    2023 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.