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Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenb\"{o}ck Spacetime with Observational Data

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Torsion can mimic dark matter without new particles, this gravity model claims.

desk verdict The paper's advertised torsion-as-CDM result is asserted rather than derived, the MCMC constraints are not actually shown, and the claimed a^-3 scaling is probably inconsistent with the fitted n≈1.95; worth a referee's time only to document why it fails. read the letter →

arxiv 2507.21359 v1 pith:FKUKJGX5 submitted 2025-07-28 gr-qc astro-ph.CO

Davood Momeni , Ratbay Myrzakulov This is my paper · ORCID
classification gr-qcastro-ph.CO
keywords darkmattertorsiongravityteleparallelF(RT)vielbeinformalismWeitzenböckspacetimecosmologicalparameterconstraintsmodified
topics Dark MatterThe Hubble Tension
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

This paper argues that dark matter need not be a particle at all. In a vielbein formulation of Weitzenböck spacetime, the torsion scalar $T$ is promoted to a dynamical field whose energy-momentum contribution is asserted to behave like a pressureless dust fluid in a uniform expanding universe. The authors fit the model with action $F(R,T)=R+\alpha T^n$ to galaxy rotation curves, CMB data, and weak-lensing measurements, obtaining best-fit values $\alpha=0.013$ and $n=1.95$. They conclude that torsion reproduces the main dark-matter observations and matches the standard cosmological model within $1\sigma$, without introducing any new particles.

What carries the argument

The load-bearing object is the torsion scalar $T$, a contraction of the torsion tensor built from the Weitzenböck connection, promoted to a dynamical field in the action $F(R,T)=R+\alpha T^n$. The paper defines an effective dark-matter energy-momentum tensor from the torsion terms in the field equations and asserts that, in a uniform expanding universe, these terms behave as a pressureless dust component. The vielbein formalism is what lets the variation treat curvature and torsion on equal footing, and the parameter $n$ controls how sharply the torsion contribution scales with the expansion.

What would settle it

Derive the Friedmann equations from the field equations and check the scaling of $T^n$: under standard teleparallel cosmology $T\propto H^2$, so $T^n\propto a^{-3n}$, and with the fitted $n=1.95$ that gives $a^{-5.85}$, not the assumed $a^{-3}$ dust scaling. A second check is to fit galaxy rotation curves with no dark halo at all and ask whether the torsion profile the theory requires reproduces each observed curve.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the torsion scalar $T$ in the Myrzakulov $F(R,T)$ action generates an effective energy-momentum tensor that mimics cold dark matter. In a uniform expanding universe this torsional contribution is asserted to scale as $\rho_{\mathrm{DM}}\sim a^{-3}$, allowing flat rotation curves and structure formation without a dark sector. The field equations, obtained by varying the vielbein, mix curvature and torsion, and the torsion contribution is identified with an effective dark-matter tensor. Fitting $F(R,T)=R+\alpha T^n$ to combined cosmological data yields $\alpha=0.013$ and $n=1.95$, and the paper reports agreement with $H_0$, $\Omega_m$, $\sigma_8$, and the matter power spectrum while offering mild relief for the $\sigma_8$ and Hubble tensions.

Load-bearing premise

The argument rests on the claim, stated without a full derivation of the modified Friedmann equations, that in a uniform expanding universe the torsion contribution behaves like pressureless dust whose density falls as the inverse cube of the scale factor; if that scaling is wrong, the geometric dark matter picture collapses.

Editorial extensions

If this is right

  • No particle dark matter candidate is needed; the dark sector is replaced by torsional geometry in the field equations.
  • The effective equation of state $w_{\mathrm{eff}}$ evolves from matter-like behavior to $w\approx-1$ at late times, giving a dynamical dark energy component rather than a constant cosmological constant.
  • The model predicts a growth index $\gamma\approx0.49$, deviating from the standard value near $0.55$, which is testable with redshift-space distortion and weak-lensing surveys.
  • Scale-dependent growth suppression at $k>0.1\,h/\mathrm{Mpc}$ and a modified integrated Sachs-Wolfe effect distinguish the model from the standard cosmological model in future CMB and lensing data.
  • Gravitational wave speed stays at $c_T\approx1$ at leading order, consistent with GW170817, but subleading torsion corrections could alter the gravitational wave luminosity distance in a way that future observatories could detect.

Reading between the lines

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

  • If torsion is the real dark matter, galactic rotation curves should show a universal torsion profile tied to the single parameter $n$, and that profile should be recoverable from the same fit across all galaxies; the paper does not test this galaxy-by-galaxy consistency.
  • The dust-scaling assumption conflicts with the standard teleparallel scaling $T\propto H^2$, since for the fitted $n=1.95$ the term $T^n$ would scale as $a^{-5.85}$ rather than $a^{-3}$; a re-derivation of the background dynamics is a direct check the authors leave open.
  • Because the pure tetrad formulation breaks local Lorentz invariance, the choice of tetrad becomes physically consequential; a covariant version with an inertial spin connection would be needed to check whether the claimed dark-matter effect survives frame changes.
  • The torsion dark matter would leave a specific imprint on gravitational-wave standard sirens, with $d_{GW}^L(z)\neq d_{EM}^L(z)$, potentially distinguishing geometric from particle dark matter with future multi-messenger observations.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. The manuscript proposes a torsion-based modified gravity model, Myrzakulov F(R,T) gravity in the vielbein formulation on Weitzenböck spacetime, in which the torsion scalar T is promoted to an effective dark matter component. The authors claim that in an FLRW background the torsion contribution behaves like pressureless dust scaling as a^{-3}, so that dark matter arises geometrically without new particles. They report an MCMC analysis over SPARC, Planck, DES, KiDS, and BOSS data for the action F = R + α T^n, with best-fit values α = 0.013, n = 1.95, Ωm = 0.311, H0 = 68.4 km/s/Mpc, and they argue that the model reproduces the observed expansion history and clustering while easing the σ8 and Hubble tensions. The paper concludes that this framework is a mathematically consistent, observationally viable, and physically elegant alternative to particle dark matter.

Significance. If the central mechanism were established, the claim that torsion in F(R,T) gravity can mimic cold dark matter without new particles would be a significant result, with testable predictions for structure growth, lensing, and cosmic acceleration. The paper also aims to provide falsifiable signatures, such as a growth index γ ≈ 0.49 and scale-dependent growth suppression, which are valuable in principle. However, the manuscript as written does not establish the central mechanism: the modified Friedmann equations are never derived from the field equations, the a^{-3} scaling is asserted without proof and appears to conflict with standard teleparallel scaling for the fitted n, and the observational analysis is presented as a single parameter table without any likelihood definition, chain diagnostics, or model predictions for the datasets. Consequently, the significance of the results cannot be assessed from the information given.

major comments (5)
  1. [Sec. III; Eqs. (10)-(11)] The central claim that torsion in an FLRW background behaves as a pressureless dust component with density scaling as a^{-3} is asserted rather than derived. The modified Friedmann equations are never obtained from the field equations in Eq. (9), and Eq. (10) is not shown to reduce to an isotropic perfect-fluid energy-momentum tensor. Moreover, under the standard teleparallel relation T = -6H^2 (which follows from the definitions in Sec. II), the action F = R + αT^n in Eq. (11) yields an effective contribution scaling as H^{2n} ∝ a^{-3n} in a matter-dominated epoch. For the reported best-fit n = 1.95, this is a^{-5.85}, not a^{-3}; the special case n = 1 gives a term that merely rescales H^2 rather than mimicking CDM. Unless the paper explicitly derives Friedmann equations from Eq. (9) that show a different scaling, the geometric dark matter mechanism is internally inconsistent with the fitted parameters.
  2. [Sec. V; Eq. (12), Table II] The observational constraint analysis is not reproducible. Equation (12) defines no actual likelihoods: L_SPARC, L_CMB, and L_LSS are never specified as functions of the model parameters, no dataset-specific theory predictions are given, and the MCMC sampler, priors, chain lengths, burn-in, and convergence diagnostics are all absent. Table II reports best-fit values and 1σ intervals without a goodness-of-fit statistic or a quantitative comparison to ΛCDM. The abstract lists SPARC, but no rotation-curve fit or galactic-scale model appears anywhere in the paper. These omissions make the claimed constraints and the statement that the model matches or improves on ΛCDM unverifiable.
  3. [Secs. III and VI; Figs. 1-2] The perturbative predictions underlying Figs. 1 and 2 and the discussion of σ8, fσ8, anisotropic stress, and the ISW effect are presented without writing the linear perturbation equations or defining how α and n enter P(k). The curves in Figs. 1-2 contain no data points, no error bars, and no description of the code used to generate them. The text in Sec. VI says that 'the marginalized contours (not shown here) indicate low degeneracy,' which contradicts the presence of the contour figures (Figs. 3-5) and further indicates that the analysis pipeline is not documented.
  4. [Sec. VI] The claims of theoretical robustness - conservation of the energy-momentum tensor, absence of ghosts, and c_T ≈ 1 to leading order - are asserted without proof. For a mixed R-T action of the form of Eq. (7), these properties are nontrivial and require explicit verification. These assertions are load-bearing for the conclusion that the model is a viable alternative to particle dark matter, but no stability analysis, Hamiltonian analysis, or perturbative wave equation is provided.
  5. [Secs. V-VI] The conclusion that the model is observationally viable because the best-fit Ωm, H0, and σ8 'fall within Planck and DES confidence regions' is circular, since Planck and DES are among the datasets used to produce the fit. No out-of-sample prediction, no Δχ² relative to ΛCDM, and no tension metric are provided. Fitting parameters to data and then reporting that the best-fit values agree with those same data does not constitute a confirmation of the model.
minor comments (6)
  1. [Throughout] The text contains repeated typographical errors, including 'FLR W' for FLRW in Secs. II-D and III, 'MyrzakulovF(R, T)' with missing space, and 'T orsion' and 'W eitzenb' in section headings.
  2. [Eq. (12)] The likelihood product in Eq. (12) is too terse; the individual likelihoods are never defined, and it is unclear how the galaxy, CMB, and LSS datasets are combined or whether their correlations are accounted for.
  3. [Figs. 3-5] The contour plots appear to be schematic; no underlying chains, sample counts, or GetDist outputs are shown, and the plots lack the detail expected for a published MCMC analysis.
  4. [References] References [22] and [28] are duplicates, as are [25] and [29]; the reference list should be consolidated and checked for consistency.
  5. [Eq. (11)] The parameter α in Eq. (11) has unspecified units; its best-fit value 0.013 is presented without dimensional analysis, which is essential for interpreting the fit and for comparing with other modified gravity constraints.
  6. [Sec. V; Table I] Table I lists Pantheon+ and Euclid as datasets, but the joint likelihood in Eq. (12) does not include them; the text should clarify which datasets were actually used in the fit.

Circularity Check

2 steps flagged · score 6.0 of 10

Observational viability is in-sample fitting presented as confirmation, and the torsion-as-CDM sector is defined into Eq. (10) and asserted to scale as a^-3 without derivation; the fitted n=1.95 contradicts that scaling.

  1. fitted input called prediction [Sec. V (Eq. 11, Eq. 12, Table II) and Sec. VII (Conclusion)]
    "To constrain the free parameters in the Myrzakulov F(R,T) torsion-based gravity model, we implement a Markov Chain Monte Carlo (MCMC) analysis combining datasets listed in Table I. ... Table II presents the best-fit values ... Our numerical analysis, based on MCMC sampling across SPARC, Planck, DES, KiDS, and BOSS datasets, reveals a region of parameter space where the model achieves excellent fits to observables such as H0, Ωm, σ8, and w_eff."

    The only model parameters (α, n) are fitted by maximizing the joint likelihood over exactly the datasets later cited as validation (SPARC, Planck, DES/KiDS, BOSS). The best-fit H0, Ωm, σ8, and w_eff are therefore in-sample outputs of the fit, not independent predictions. Calling this an 'excellent fit' to the same data used in the likelihood is confirmation by construction: any flexible model will reproduce the data it was tuned on. No out-of-sample test, train/test split, or model-comparison statistic (Δχ² per degree of freedom) is supplied to make the agreement informative.

  2. self definitional [Sec. III, Eq. (10) and following paragraphs]
    "We define the effective dark matter energy-momentum tensor via the torsion contributions: T^(DM)_{μν} ≡ (1/κ²)( F_T S^ν_{ρμ} ∇^ρ T + (1/e) ∂_ρ(e F_T S^ν_{ρμ}) ). (10) This term behaves as a pressureless fluid under appropriate symmetry assumptions (e.g., FLRW metric or spherically symmetric configurations)."

    The object that is later said to replace particle dark matter is introduced by definition as the torsion-sector terms of the field equations. The conclusion 'torsion mimics CDM' is then partly a relabeling of those terms as a dark-matter tensor. The quantitative requirement for CDM—ρ_eff ∝ a^{-3}—is asserted in the same section ('torsion contributions scale similarly to ρ_CDM ∼ a^{-3}') without inserting the FLRW tetrad into Eq. (9) or writing the modified Friedmann equations. With the fitted action F=R+αT^n and the standard teleparallel FLRW identity T=-6H^2, T^n scales as a^{-3n}, i.e., a^{-5.85} at n=1.95, so the asserted a^{-3} scaling is not a consequence of the model's own best-fit parameters.

full rationale

The central claim of an observationally viable geometric dark matter is made circular in two ways. First, the free parameters of F(R,T)=R+αT^n (α,n) and the background parameters are fitted to the same SPARC/Planck/DES/KiDS/BOSS data that are later reported as 'excellent fits'; this is in-sample validation, so the agreement is enforced rather than predicted. Second, the effective dark-matter tensor is defined as the torsion part of the field equations (Eq. 10), and its pressureless CDM-like behavior (ρ∝a^{-3}) is asserted rather than derived; the assertion is moreover inconsistent with the fitted n≈1.95 under T=-6H^2. The heavy reliance on the authors' own prior papers (refs. [6], [8], [9], [10]) for the 'Myrzakulov gravity' framework is a self-referential program but is secondary: the equations are stated in the text and could in principle be checked independently. A score of 6 reflects that some predictions (w_eff(z), P(k), γ≈0.49, ISW and anisotropic-stress signatures) are conditional outputs that could be tested in future surveys, so the paper is not wholly equivalent to its inputs; however, the main 'viability' conclusion reduces to a fit, and the core DM mechanism is definitional/asserted. The ρ∝a^{-3} scaling gap is also a correctness risk, distinct from circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The model depends on two fitted parameters (α, n), plus standard fitted cosmological parameters, and on several unproved assumptions: the correctness of the vielbein field equations, the dust-like scaling of the torsion fluid, and the existence of torsion-enhanced clustering. The paper introduces an effective torsion fluid as a stand-in for dark matter, but provides no independent falsifiable handle beyond the asserted fits.

free parameters (4)
  • α = 0.013 [0.010, 0.017]
    Coupling constant of the torsion term in F=R+αT^n; fitted to combined cosmological data, central to every fit claim.
  • n = 1.95 [1.84, 2.08]
    Power of the torsion scalar; fitted to data. The claimed CDM-like behavior depends critically on this exponent.
  • Ωm = 0.311 [0.295, 0.326]
    Standard matter density parameter fitted jointly with the model parameters in the MCMC.
  • H0 = 68.4 km/s/Mpc [67.3, 69.6]
    Hubble constant fitted jointly with the model parameters; used to judge compatibility with ΛCDM.
assumptions (4)
  • domain assumption The vielbein field equations (Eq. 9) are correct and complete.
    No derivation is shown; every phenomenological statement in the paper depends on these equations.
  • ad hoc to paper In FLRW, the torsion scalar T produces a perfect-fluid contribution scaling as cold dark matter with density proportional to a^-3.
    Asserted in Sec. III without derivation; under standard T∼H^2 scaling the fitted n=1.95 would give a different scaling.
  • ad hoc to paper The modified Poisson equation sourced by torsion enhances matter clustering similarly to dark matter halos.
    Stated in Sec. III with no equations or analysis to support it.
  • domain assumption The energy-momentum tensor is conserved in this formulation.
    Asserted in the Introduction and Sec. VI without proof; governs the matter coupling and the validity of the fluid interpretation.
invented entities (2)
  • Effective torsion dark matter energy-momentum tensor T^(DM)_μν (Eq. 10)
    purpose: Acts as the geometric source replacing particle dark matter in galaxy rotation curves, CMB observables, and lensing.
    No independent falsifiable prediction is computed; the tensor is defined by analogy and its scaling asserted, not derived.
  • Torsion-induced effective dark matter fluid with dust-like scaling
    purpose: Mimics cold dark matter in the Friedmann equations and structure growth.
    The scaling is asserted in Sec. III; no background equations are shown, so the fluid is an interpretive construction with no external handle.

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Cite this review

Pith. "Pith review of Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenb\"{o}ck Spacetime with Observational Data." pith.science (2026). https://pith.science/paper/FKUKJGX5

@misc{pith2026250721359,
  author       = {Pith},
  title        = {Pith review of: Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenb\"ock Spacetime with Observational Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FKUKJGX5}},
  note         = {Machine review of arXiv:2507.21359}
}
abstract

We explore dark matter phenomenology in Myrzakulov $F(R,T)$ gravity, formulated via the vielbein approach in Weitzenb\"{o}ck spacetime. In this torsion-based extension of gravity, dark matter emerges as a geometric effect rather than a particle species, with curvature and torsion contributing dynamically to the field equations. Using recent data -- including SPARC galaxy rotation curves, Planck CMB observations, and weak lensing from DES and KiDS -- we constrain the model through MCMC analysis. Our results show that, under specific parameter choices, the theory replicates key cosmological features without introducing additional dark sector matter. This framework offers a testable alternative to $\Lambda$CDM, providing new insight into structure formation, gravitational lensing, and cosmic acceleration -- all rooted in the geometry of spacetime.

Figures

Figures reproduced from arXiv: 2507.21359 by the authors.

Figure 1
Figure 1. FIG. 1: Effective equation of state [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Matter power spectrum [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Posterior confidence contours for model parameters [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Posterior confidence contours for [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Posterior confidence contours for [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.