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arxiv: 2604.10061 · v1 · submitted 2026-04-11 · 🌀 gr-qc

Cosmological Parameters in f(T) Gravity: Theoretical and Observational Analysis

Suraj Kumar Behera , S. A. Kadam , Pratik P. Ray , B. Mishra This is my paper

Pith reviewed 2026-05-10 16:31 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(T) gravityteleparallel gravitydynamical systemscosmological parametersMCMC constraintsBAO datacosmic expansion
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The pith

A torsion-based gravity model with chosen power-law terms reproduces the observed cosmic expansion history when its parameters satisfy stability conditions from dynamical analysis.

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

The paper studies an extension of teleparallel gravity by adopting the form f(T) = αT − β u^{-n} + γ u^m, with u defined as negative T divided by six. The cosmological equations are recast as an autonomous dynamical system whose critical points correspond to radiation-dominated, matter-dominated, and late-time accelerating phases. Stability analysis shows these points are stable when the exponents obey m less than one and n greater than negative one. Markov Chain Monte Carlo fitting to DESI DR2 baryon acoustic oscillation measurements combined with Hubble and Pantheon+SH0ES supernova data yields best-fit values m approximately 0.91 and n approximately 0.69, which lie inside the stable interval. The combined results indicate that this single function of torsion can drive the full sequence of cosmic epochs without separate dark-energy components.

Core claim

With the functional form f(T) = αT − βu^{-n} + γu^m, phase-space analysis identifies critical points for the radiation, matter, and dark-energy eras whose stability holds for m < 1 and n > −1. MCMC constraints from DESI DR2 BAO together with Hubble and Pantheon+SH0ES data return m = 0.91^{+0.07}_{-0.09} and n = 0.69^{+0.09}_{-0.08}, values inside the stable range, so that the model reproduces the observed cosmic expansion history.

What carries the argument

The autonomous system formed by rewriting the Friedmann equations of f(T) gravity, whose fixed points classify the evolutionary epochs and whose stability bounds are compared against MCMC-fitted parameter values.

If this is right

  • The model passes through stable radiation, matter, and accelerating phases in the required order.
  • Late-time acceleration is produced by the u^m term when m is positive but less than one.
  • The observationally preferred values of m and n automatically satisfy the stability criteria derived from the autonomous system.
  • No extra scalar field or cosmological constant is required to explain the current acceleration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the functional form proves general, the same approach could be applied to growth-of-structure data to test whether the model remains consistent beyond background expansion.
  • The linkage of early and late behavior through a single torsion function might address why the dark-energy density becomes important only recently.
  • Tighter future bounds on the Hubble parameter could narrow the allowed window for n and m and reveal whether the stability window shrinks or survives.

Load-bearing premise

The chosen combination of linear, inverse-power, and positive-power terms in f(T) is general enough to capture the dynamics needed for a realistic cosmology.

What would settle it

An independent measurement of the expansion rate that forces the best-fit m above 1 or n below −1 while still matching the data would falsify the model's ability to remain stable across epochs.

Figures

Figures reproduced from arXiv: 2604.10061 by B. Mishra, Pratik P. Ray, S. A. Kadam, Suraj Kumar Behera.

Figure 1
Figure 1. Figure 1: Phase space diagram of the autonomous system showing the critical points [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The evolution of EoS parameters, density and deceleration parameter as functions of redshift with the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A two-dimensional contour diagram derived from the observational [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A two-dimensional contour diagram derived from the Pantheon+SH0ES analysis, depicting best-fit [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A two-dimensional contour diagram derived from the DESI DR2 BAO analysis, depicting best-fit [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A two-dimensional contour diagram derived from the combined ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (i) Left panel: Redshift evolution of the Hubble parameter with corresponding error bars; (ii) Right panel: Distance modulus as a function of redshift including observational uncertainties. analysis, and a stable accelerating cosmological model is achieved by integrating torsion instead of curvature and f(T) form. The observational analysis strengthened this theoretical investigation by fitting the extract… view at source ↗
read the original abstract

The $f(T)$ gravity is one of the extensions of teleparallel equivalent of general relativity, in which more general functions of the torsion scalar $T$ can be described. With the proposed functional form of $f(T) = \alpha T - \beta u^{-n} + \gamma u^m$, where $u = (-T/6)$, we have analyzed the cosmological parameters using dynamical system analysis and cosmological datasets. The dynamical behavior of this model is analyzed with phase-space analysis by transforming the cosmological equations into an autonomous system. Critical points are identified, and their stability conditions examined, enabling the classifications of the early and late-time evolutionary phases of the Universe. The stability conditions are further demonstrated by phase-portrait diagrams that highlight transitions between radiation, matter, and dark-energy-dominated epochs. Then we used the Markov Chain Monte Carlo statistical technique to constrain the model parameters with the recent observational dataset, such as DESI DR2 BAO, and its combination with the Hubble and Pantheon+SH0ES data. The best-fit values for the model parameters were obtained by data analysis, $m \equiv 0.91^{+0.07}_{-0.09}$ and $n \equiv 0.69^{+0.09}_{-0.08}$, and are well within the stability range obtained ($m<1\land n>-1$) through dynamical system analysis. The combined theoretical and observational analysis shows that the proposed $f(T)$ gravity model successfully reproduces the observed cosmic expansion history of the Universe.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the specific f(T) form f(T) = αT − βu^{-n} + γu^m (u = −T/6), converts the background cosmological equations to an autonomous dynamical system, identifies critical points and derives stability conditions m < 1 and n > −1 that permit a radiation → matter → dark-energy sequence, presents phase portraits confirming the transitions, and performs MCMC parameter estimation on DESI DR2 BAO combined with Hubble and Pantheon+SH0ES data, obtaining best-fit values m = 0.91^{+0.07}_{-0.09}, n = 0.69^{+0.09}_{-0.08} that lie inside the stability window, thereby claiming the model reproduces the observed expansion history.

Significance. If the derivations are correct, the work supplies a concrete, observationally viable f(T) model whose parameters are simultaneously constrained by data and shown to satisfy analytically derived stability requirements for the full cosmic sequence. The explicit consistency check between the MCMC posterior and the pre-data stability bounds, together with the use of recent DESI DR2 data, constitutes a clear strength of the combined theoretical–observational approach.

major comments (2)
  1. [Dynamical system analysis] Dynamical system analysis: the autonomous system obtained from the Friedmann and torsion equations, the coordinates of the critical points, and the Jacobian matrix whose eigenvalues yield the stability conditions m < 1 and n > −1 are not displayed. Without these explicit expressions it is impossible to reproduce the phase portraits or to confirm that the reported best-fit values lie in the stable region by direct substitution rather than by assertion.
  2. [MCMC constraints] Observational analysis: the explicit likelihood function, the precise combination of DESI DR2 BAO + Hubble + Pantheon+SH0ES, and any priors or nuisance parameters employed in the MCMC are not stated. This information is load-bearing for verifying that the quoted best-fit values and uncertainties for m and n are correctly derived and that no post-hoc data selection affects the conclusion that they satisfy m < 1, n > −1.
minor comments (2)
  1. [Introduction] The notation u = −T/6 is introduced without a brief reminder of its relation to the torsion scalar in the teleparallel framework; adding one sentence would improve readability for readers outside the immediate subfield.
  2. [Phase portraits] Figure captions for the phase portraits should explicitly label the axes in terms of the autonomous variables and indicate which critical points correspond to radiation, matter, and dark-energy domination.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate the requested details for improved reproducibility.

read point-by-point responses

  1. Referee: [Dynamical system analysis] Dynamical system analysis: the autonomous system obtained from the Friedmann and torsion equations, the coordinates of the critical points, and the Jacobian matrix whose eigenvalues yield the stability conditions m < 1 and n > −1 are not displayed. Without these explicit expressions it is impossible to reproduce the phase portraits or to confirm that the reported best-fit values lie in the stable region by direct substitution rather than by assertion.

    Authors: We agree that the explicit autonomous system, critical point coordinates, and Jacobian matrix were omitted from the original submission, which limits independent verification. In the revised manuscript we have added a new subsection that derives the autonomous system from the Friedmann and torsion equations, lists all critical points with their coordinates, and presents the full Jacobian matrix. The eigenvalues are computed explicitly, confirming the stability conditions m < 1 and n > −1. We also substitute the MCMC best-fit values (m = 0.91, n = 0.69) directly into these conditions and report the result, together with updated phase portraits that reference the new expressions. revision: yes

  2. Referee: [MCMC constraints] Observational analysis: the explicit likelihood function, the precise combination of DESI DR2 BAO + Hubble + Pantheon+SH0ES, and any priors or nuisance parameters employed in the MCMC are not stated. This information is load-bearing for verifying that the quoted best-fit values and uncertainties for m and n are correctly derived and that no post-hoc data selection affects the conclusion that they satisfy m < 1, n > −1.

    Authors: We acknowledge that the MCMC methodology was not described in sufficient detail. The revised manuscript now includes the explicit likelihood function, the precise dataset combination (DESI DR2 BAO together with Hubble and Pantheon+SH0ES), the priors on all parameters (including m and n), and any nuisance parameters. We confirm that no post-hoc data selection was performed and that the posterior samples satisfy the stability window m < 1, n > −1 derived from the dynamical analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent dynamical analysis and external data

full rationale

The paper selects a functional form for f(T), converts the Friedmann equations into an autonomous dynamical system, derives stability conditions (m < 1, n > -1) from the critical-point analysis, and separately performs MCMC fitting to external datasets (DESI DR2 BAO, Hubble, Pantheon+SH0ES). The best-fit parameters lie inside the previously derived stability region and the phase portraits recover the expected radiation-matter-DE sequence. Neither the stability bounds nor the expansion history are obtained by re-expressing the fitted values; the dynamical-system results are obtained prior to and independently of the data fit. No self-citation chain, self-definitional step, or fitted-input-renamed-as-prediction is present. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the chosen f(T) ansatz is physically motivated and that standard FLRW cosmology plus teleparallel equivalence holds. No new particles or forces are postulated.

free parameters (3)
  • m
    Exponent in the positive-power term; fitted to data and required to satisfy m < 1 for stability.
  • n
    Exponent in the negative-power term; fitted to data and required to satisfy n > −1 for stability.
  • α, β, γ
    Overall scaling coefficients whose values are implicitly absorbed into the normalization of the Hubble parameter during fitting.
axioms (2)
  • domain assumption The universe is described by a flat FLRW metric and the torsion scalar T is the only gravitational degree of freedom.
    Standard assumption in f(T) cosmology invoked throughout the dynamical-system analysis.
  • standard math The matter content is perfect fluid with standard equation-of-state parameters for radiation and dust.
    Used to close the autonomous system of equations.

pith-pipeline@v0.9.0 · 5587 in / 1520 out tokens · 39525 ms · 2026-05-10T16:31:17.371570+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · 1 internal anchor

  1. [1]

    γum 3H2 1 2 −m +α # =1 . (19) We substitute, Ωm = κ2ρm 3H2 ,r= κ2ρr 3H2 ,x= βu−n 3H2 1 2 +n ,y=−

    and so on. The cosmological perturbation has been analyzed in Ref. [39–42]. The finite-time future singularity inf(T)gravity has been shown in [43], whereas the Noether symmetry approach to find an exact solution to the given Lagrangian is significant [44, 45]. Zheng and Huang [46] have compared the power-law framed model and the observable prediction ofΛ...

    work page 2023

  2. [2]

    Cosmological parameters from sdss and wmap,

    M. Tegmark, M. A. Strauss,et al., “Cosmological parameters from sdss and wmap,”Physical Review D69(2004) 103501

    work page 2004

  3. [3]

    Detection of the baryon acoustic peak in the large-scale correlation function of sdss luminous red galaxies,

    D. J. Eisenstein and et al., “Detection of the baryon acoustic peak in the large-scale correlation function of sdss luminous red galaxies,”Astrophysical Journal633(2005) 560

    work page 2005

  4. [4]

    First-year wilkinson microwave anisotropy probe (wmap) observations: Determination of cosmological parameters,

    D. N. Spergel and et al., “First-year wilkinson microwave anisotropy probe (wmap) observations: Determination of cosmological parameters,”Astrophysical Journal Supplement Series148(2003) 175

    work page 2003

  5. [5]

    Three-year wilkinson microwave anisotropy probe (wmap) observations: Implications for cosmology,

    D. N. Spergel and et al., “Three-year wilkinson microwave anisotropy probe (wmap) observations: Implications for cosmology,”Astrophysical Journal Supplement Series170(2007) 377. 14

    work page 2007

  6. [6]

    Observational evidence from supernovae for an accelerating universe and a cosmological constant,

    A. G. Riess, A. V . Filippenko, P . Challis,et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,”The Astronomical Journal116(1998) 1009–1038

    work page 1998

  7. [7]

    Measurements ofωandλfrom 42 high-redshift supernovae,

    S. Perlmutter, G. Aldering, G. Goldhaber,et al., “Measurements ofωandλfrom 42 high-redshift supernovae,”The Astrophysical Journal517(1999) 565–586

    work page 1999

  8. [8]

    Effective field theory, black holes, and the cosmological constant,

    A. G. Cohen, D. B. Kaplan, and A. E. Nelson, “Effective field theory, black holes, and the cosmological constant,”Physical Review Letters82(1999) 4971

    work page 1999

  9. [9]

    A model of holographic dark energy,

    M. Li, “A model of holographic dark energy,”Phys. Lett. B603(2004) no. 1, 1

    work page 2004

  10. [10]

    Cosmological constraints on new agegraphic dark energy,

    H. Wei and R.-G. Cai, “Cosmological constraints on new agegraphic dark energy,”Phys. Lett. B663(2008) no. 1, 1

    work page 2008

  11. [11]

    A new model of agegraphic dark energy,

    H. Wei and R.-G. Cai, “A new model of agegraphic dark energy,”Phys. Lett. B660(2008) no. 3, 113

    work page 2008

  12. [12]

    Holographic dark energy model from ricci scalar curvature,

    C. Gao and et al., “Holographic dark energy model from ricci scalar curvature,”Physical Review D79(2009) 043511

    work page 2009

  13. [13]

    Cosmological imprint of an energy component with general equation of state,

    R. R. Caldwell, R. Dave, and P . J. Steinhardt, “Cosmological imprint of an energy component with general equation of state,”Physical Review Letters80(1998) 1582

    work page 1998

  14. [14]

    A phantom menace? cosmological consequences of a dark energy component with super-negative equation of state,

    R. R. Caldwell, “A phantom menace? cosmological consequences of a dark energy component with super-negative equation of state,”Physics Letters B545(2002) 23

    work page 2002

  15. [15]

    Essentials of k-essence,

    C. Armendariz-Picon, V . Mukhanov, and P . J. Steinhardt, “Essentials of k-essence,”Physical Review D63(2001) 103510

    work page 2001

  16. [16]

    Accelerated expansion of the universe driven by tachyonic matter,

    T. Padmanabhan, “Accelerated expansion of the universe driven by tachyonic matter,”Physical Review D66(2002) 021301

    work page 2002

  17. [17]

    Remarks on tachyon driven cosmology,

    A. Sen, “Remarks on tachyon driven cosmology,”Physica Scripta2005(2005) 70

    work page 2005

  18. [18]

    Late-time cosmology in a (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up,

    E. Elizalde, S. ichi Nojiri, and S. D. Odintsov, “Late-time cosmology in a (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up,”Physical Review D70(2004) 043539

    work page 2004

  19. [19]

    Dark energy constraints from the cosmic age and supernova,

    B. Feng, X. Wang, and X. Zhang, “Dark energy constraints from the cosmic age and supernova,”Physics Letters B607(2005) 35

    work page 2005

  20. [20]

    An alternative to quintessence,

    A. Kamenshchik, U. Moschella, and V . Pasquier, “An alternative to quintessence,”Physics Letters B511(2001) 265

    work page 2001

  21. [21]

    Generalized chaplygin gas, accelerated expansion, and dark-energy–matter unification,

    M. C. Bento, O. Bertolami, and A. A. Sen, “Generalized chaplygin gas, accelerated expansion, and dark-energy–matter unification,”Physical Review D66(2002) 043507

    work page 2002

  22. [22]

    The cosmological constant,

    S. M. Carroll, “The cosmological constant,”Living Reviews in Relativity4(2001) 1

    work page 2001

  23. [23]

    Dynamics of dark energy,

    E. J. Copeland, M. Sami, and S. Tsujikawa, “Dynamics of dark energy,”International Journal of Modern Physics D15(2006) 1753

    work page 2006

  24. [24]

    Inflation dynamics and reheating,

    B. A. Bassett, S. Tsujikawa, and D. Wands, “Inflation dynamics and reheating,”Reviews of Modern Physics78(2006) 537

    work page 2006

  25. [25]

    Quintom cosmology: Theoretical implications and observations,

    Y.-F. Cai and et al., “Quintom cosmology: Theoretical implications and observations,”Physics Reports493(2010) 1

    work page 2010

  26. [26]

    Extended theories of gravity,

    S. Capozziello and M. De Laurentis, “Extended theories of gravity,”Physics Reports509(2011) 167–321

    work page 2011

  27. [27]

    The cosmoverse white paper: Addressing observational tensions in cosmology with systematics and fundamental physics,

    E. Di Valentinoet al., “The cosmoverse white paper: Addressing observational tensions in cosmology with systematics and fundamental physics,”Physics of the Dark Universe49(2025) 101965

    work page 2025

  28. [28]

    Introduction to teleparallel gravities,

    A. Golovnev, “Introduction to teleparallel gravities,”arXiv preprint arXiv:1801.06929(2018)

    work page arXiv 2018

  29. [29]

    Born-infeld gravity in weitzenb ¨ock spacetime,

    R. Ferraro and F. Fiorini, “Born-infeld gravity in weitzenb ¨ock spacetime,”Physical Review D78(2008) 124019

    work page 2008

  30. [30]

    Dark torsion as the cosmic speed-up,

    G. R. Bengochea and R. Ferraro, “Dark torsion as the cosmic speed-up,”Physical Review D79(2009) 124019

    work page 2009

  31. [31]

    Einstein’s other gravity and the acceleration of the universe,

    E. V . Linder, “Einstein’s other gravity and the acceleration of the universe,”Physical Review D81(2010) 127301

    work page 2010

  32. [32]

    Teleparallel theories of gravity: illuminating a fully invariant approach,

    M. Krssak, R. J. van den Hoogen, J. G. Pereira, C. G. B ¨ohmer, and A. A. Coley, “Teleparallel theories of gravity: illuminating a fully invariant approach,”Class. Quant. Grav.36(2019) no. 18, 183001

    work page 2019

  33. [33]

    Teleparallel gravity: From theory to cosmology,

    S. Bahamonde and et al., “Teleparallel gravity: From theory to cosmology,”Reports on Progress in Physics86(2023) 026901

    work page 2023

  34. [34]

    Accelerating Universe fromF(T)Gravity,

    R. Myrzakulov, “Accelerating Universe fromF(T)Gravity,”European Physical Journal C71(2011) 1752

    work page 2011

  35. [35]

    f(T)Gravity Mimicking Dynamical Dark Energy: Background and Perturbation Analysis,

    J. B. Dent, S. Dutta, and E. N. Saridakis, “f(T)Gravity Mimicking Dynamical Dark Energy: Background and Perturbation Analysis,”Journal of Cosmology and Astroparticle Physics2011(2011) 009

    work page 2011

  36. [36]

    Observational Information forf(T)Theories and Dark Torsion,

    G. R. Bengochea, “Observational Information forf(T)Theories and Dark Torsion,”Physics Letters B695(2011) 405

    work page 2011

  37. [37]

    Observational Constraints onf(T)Theory,

    P . Wu and H. Yu, “Observational Constraints onf(T)Theory,”Physics Letters B693(2010) 415

    work page 2010

  38. [38]

    Notes onf(T)theories,

    Y. Zhanget al., “Notes onf(T)theories,”J. Cosmol. Astropart. Phys.2011(2011) no. 07, 015

    work page 2011

  39. [39]

    f(T)Theories and Varying Fine Structure Constant,

    H. Wei, X.-P . Ma, and H.-Y. Qi, “f(T)Theories and Varying Fine Structure Constant,”Physics Letters B703(2011) 74

    work page 2011

  40. [40]

    Cosmological Perturbations inf(T)Gravity,

    S.-H. Chen and et al., “Cosmological Perturbations inf(T)Gravity,”Physical Review D83(2011) 023508

    work page 2011

  41. [41]

    Matter Bounce Cosmology with thef(T)Gravity,

    Y.-F. Cai and et al., “Matter Bounce Cosmology with thef(T)Gravity,”Classical and Quantum Gravity28(2011) 215011

    work page 2011

  42. [42]

    Propagating gravitational waves in teleparallel Gauss-Bonnet gravity,

    S. K. Mishra, J. L. Said, and B. Mishra, “Propagating gravitational waves in teleparallel Gauss-Bonnet gravity,”Phys. Rev. D 112(2025) 064019

    work page 2025

  43. [43]

    Gauge invariant perturbations of $F(T,T_G)$ Cosmology

    S. K. Mishra, J. L. Said, and B. Mishra, “Gauge invariant perturbations ofF(T,T G)Cosmology,”arXiv:2509.02646 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  44. [44]

    Reconstruction off(T)Gravity: Rip Cosmology, Finite-Time Future Singularities, and Thermodynamics,

    K. Bamba and et al., “Reconstruction off(T)Gravity: Rip Cosmology, Finite-Time Future Singularities, and Thermodynamics,”Physical Review D85(2012) 104036

    work page 2012

  45. [45]

    Noether Symmetry inf(T)Theory,

    H. Wei, X.-J. Guo, and L.-F. Wang, “Noether Symmetry inf(T)Theory,”Physics Letters B707(2012) 298

    work page 2012

  46. [46]

    Noether Symmetry ofF(T)Cosmology with Quintessence and Phantom Scalar Fields,

    M. Jamil, D. Momeni, and R. Myrzakulov, “Noether Symmetry ofF(T)Cosmology with Quintessence and Phantom Scalar Fields,”European Physical Journal C72(2012) 2137. 15

    work page 2012

  47. [47]

    Growth Factor inf(T)Gravity,

    R. Zheng and Q.-G. Huang, “Growth Factor inf(T)Gravity,”Journal of Cosmology and Astroparticle Physics2011(2011) 002

    work page 2011

  48. [48]

    Canf(T)Gravity Theories MimicΛCDM Cosmic History,

    M. R. Setare and N. Mohammadipour, “Canf(T)Gravity Theories MimicΛCDM Cosmic History,”Journal of Cosmology and Astroparticle Physics2013(2013) 015

    work page 2013

  49. [49]

    Static Solutions with Spherical Symmetry inf(T)Theories,

    T. Wang, “Static Solutions with Spherical Symmetry inf(T)Theories,”Physical Review D84(2011) 024042

    work page 2011

  50. [50]

    Phase-space analysis of teleparallel dark energy,

    C. Xu, E. N. Saridakis, and G. Leon, “Phase-space analysis of teleparallel dark energy,”Journal of Cosmology and Astroparticle Physics2012(2012) 005

    work page 2012

  51. [51]

    Equation of State for Dark Energy inf(T)Gravity,

    K. Bamba and et al., “Equation of State for Dark Energy inf(T)Gravity,”Journal of Cosmology and Astroparticle Physics2011 (2011) 021

    work page 2011

  52. [52]

    f(T)Models with Phantom Divide Line Crossing,

    P . Wu and H. Yu, “f(T)Models with Phantom Divide Line Crossing,”European Physical Journal C71(2011) 1552

    work page 2011

  53. [53]

    Bayesian Analysis off(T)Gravity Usingfσ 8 Data,

    F. K. Anagnostopoulos, S. Basilakos, and E. N. Saridakis, “Bayesian Analysis off(T)Gravity Usingfσ 8 Data,”Physical Review D100(2019) 083517

    work page 2019

  54. [54]

    Testing the Violation of the Equivalence Principle in the Electromagnetic Sector and Its Consequences inf(T)Gravity,

    J. L. Said and et al., “Testing the Violation of the Equivalence Principle in the Electromagnetic Sector and Its Consequences inf(T)Gravity,”Journal of Cosmology and Astroparticle Physics2020(2020) 047

    work page 2020

  55. [55]

    Model-independent Reconstruction off(T)Gravity from Gaussian Processes,

    Y.-F. Cai, M. Khurshudyan, and E. N. Saridakis, “Model-independent Reconstruction off(T)Gravity from Gaussian Processes,”Astrophysical Journal888(2020) 62

    work page 2020

  56. [56]

    Constraining teleparallel gravity through gaussian processes,

    R. Briffa and et al., “Constraining teleparallel gravity through gaussian processes,”Classical and Quantum Gravity38(2021) 055007

    work page 2021

  57. [57]

    Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data,

    J. L. Said and et al., “Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data,”Journal of Cosmology and Astroparticle Physics2021(2021) 015

    work page 2021

  58. [58]

    Constrainingf(T)gravity by dynamical system analysis,

    B. Mirza and F. Oboudiat, “Constrainingf(T)gravity by dynamical system analysis,”J. Cosmol. Astropart. Phys.2017(2017) no. 11, 011

    work page 2017

  59. [59]

    Dynamical stability analysis of acceleratingf(T)gravity models,

    L. K. Duchaniya, S. V . Lohakare, B. Mishra, and S. K. Tripathy, “Dynamical stability analysis of acceleratingf(T)gravity models,”Eur. Phys. J. C82(2022) no. 5, 448

    work page 2022

  60. [60]

    Attractor behavior off(T)modified gravity and the cosmic acceleration,

    L. Duchaniya, K. Gandhi, and B. Mishra, “Attractor behavior off(T)modified gravity and the cosmic acceleration,”Physics of the Dark Universe44(2024) 101461

    work page 2024

  61. [61]

    Dynamical systems in cosmology,

    C. G. B ¨ohmer and N. Chan, “Dynamical systems in cosmology,” inDynamical and Complex Systems, pp. 121–156. World Scientific, 2017

    work page 2017

  62. [62]

    Dynamical system analysis in teleparallel gravity with boundary term,

    S. A. Kadam, N. P . Thakkar, and B. Mishra, “Dynamical system analysis in teleparallel gravity with boundary term,”Eur. Phys. J. C83(2023) no. 9,

    work page 2023

  63. [63]

    Dynamical systems analysis inf(T,ϕ)gravity,

    L. K. Duchaniya, S. A. Kadam, J. L. Said, and B. Mishra, “Dynamical systems analysis inf(T,ϕ)gravity,”Eur. Phys. J. C83 (2023) no. 1, 27

    work page 2023

  64. [64]

    Teleparallel scalar-tensor gravity through cosmological dynamical systems,

    S. A. Kadam, B. Mishra, and J. Said Levi, “Teleparallel scalar-tensor gravity through cosmological dynamical systems,”Eur. Phys. J. C82(2022) no. 8, 680

    work page 2022

  65. [65]

    Cosmological solutions off(T)gravity,

    A. Paliathanasis, J. D. Barrow, and P . G. L. Leach, “Cosmological solutions off(T)gravity,”Phys. Rev. D94(2016) no. 2, 023525

    work page 2016

  66. [66]

    New general relativity,

    K. Hayashi and T. Shirafuji, “New general relativity,”Phys. Rev. D19(1979) 3524. Addendum: Phys. Rev. D 24, 3312 (1982)

    work page 1979

  67. [67]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation. W. H. Freeman, San Francisco, 1973

    work page 1973

  68. [68]

    New types off(T)gravity,

    R.-J. Yang, “New types off(T)gravity,”Eur. Phys. J. C71(2011) no. 11, 1797

    work page 2011

  69. [69]

    Dynamical complexity of the teleparallel gravity cosmology,

    G. A. Rave-Franco, C. Escamilla-Rivera, and J. L. Said, “Dynamical complexity of the teleparallel gravity cosmology,”Phys. Rev. D103(2021) no. 8, 084017

    work page 2021

  70. [70]

    Stability analysis for cosmological models inf(T,B)gravity,

    G. A. Rave-Franco, C. Escamilla-Rivera, and J. L. Said, “Stability analysis for cosmological models inf(T,B)gravity,”Eur. Phys. J. C80(2020) no. 7, 677

    work page 2020

  71. [71]

    Cosmological dynamics of dark energy in scalar-torsionf(T,ϕ)gravity,

    M. Gonzalez-Espinoza and G. Otalora, “Cosmological dynamics of dark energy in scalar-torsionf(T,ϕ)gravity,”Eur. Phys. J. C81(2021) no. 5, 480

    work page 2021

  72. [72]

    Constrainingf(T,B,T G,B G)gravity by dynamical system analysis,

    S. A. Kadam and B. Mishra, “Constrainingf(T,B,T G,B G)gravity by dynamical system analysis,”Phys. Dark Universe46 (2024) 101693

    work page 2024

  73. [73]

    Teleparallel gravity and quintessence: The role of nonminimal boundary couplings,

    S. A. Kadam, L. K. Duchaniya, and B. Mishra, “Teleparallel gravity and quintessence: The role of nonminimal boundary couplings,”Ann. Phys.470(2024) 169808

    work page 2024

  74. [74]

    Cosmology inf(Q)gravity: A unified dynamical systems analysis of the background and perturbations,

    W. Khyllepet al., “Cosmology inf(Q)gravity: A unified dynamical systems analysis of the background and perturbations,”Phys. Rev. D107(2023) no. 4, 044022. [74]PlanckCollaboration, N. Aghanimet al., “Planck 2018 results. VI. Cosmological parameters,”Astron. Astrophys.641(2020) A6. [Erratum: Astron.Astrophys. 652, C4 (2021)]

    work page 2023

  75. [75]

    Cosmographic bounds on the cosmological deceleration–acceleration transition redshift inf(R) gravity,

    S. Capozzielloet al., “Cosmographic bounds on the cosmological deceleration–acceleration transition redshift inf(R) gravity,”Phys. Rev. D90(2014) no. 4, 044016

    work page 2014

  76. [76]

    Local determination of the hubble constant and the deceleration parameter,

    D. Camarena and V . Marra, “Local determination of the hubble constant and the deceleration parameter,”Phys. Rev. Res.2 (2020) 013028. 16

    work page 2020

  77. [77]

    Weyl-typef(Q,T)gravity observationally constrained cosmological models,

    R. Bhagat, S. A. Narawade, and B. Mishra, “Weyl-typef(Q,T)gravity observationally constrained cosmological models,” Phys. Dark Universe41(2023) 101250

    work page 2023

  78. [78]

    The pantheon+ analysis: Cosmological constraints,

    D. Broutet al., “The pantheon+ analysis: Cosmological constraints,”Astrophys. J.938(2022) 110

    work page 2022

  79. [79]

    DESI DR2 Results. II. Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,

    M. Abdul Karimet al., “DESI DR2 Results. II. Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,”Phys. Rev. D112(2025) 083515

    work page 2025