{"id":"7a4fa163-3c0b-4d97-9fef-199bf2a22416","arxiv_id":"2507.21359","paper_version":1,"verdict":"REJECT","confidence":"LOW","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"The paper claims a torsion-based F(R,T) model can replace dark matter but provides no derivations, likelihoods, or data, leaving the claim unsupported.","lead":"A modified gravity paper claims a torsion scalar in F(R,T) gravity can replace dark matter, with MCMC fits to SPARC, Planck, DES, and KiDS data. The paper does not show the likelihood, the derived cosmological equations, or any rotation-curve calculation, so the central claim is currently unsubstantiated.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim that torsion mimics CDM is asserted, not derived; with F=R+αT^n and standard T∝H^2 in FLRW, the fitted n≈1.95 gives ρ_T∝a^{-5.85}, not a^{-3}, so the geometric-DM mechanism is unsupported and likely inconsistent.","rationale":"The reader's weakest assumption correctly identifies the unproved and likely false scaling of the torsion contribution as the pivotal point. I see no independent support in the manuscript that could offset this: there is no machine-checked derivation, no released code or data, and no parameter-free prediction. The paper's Eq. (9) is presented as the final field equations, but it is never used to derive any cosmological background, and the effective dark-matter energy-momentum tensor in Eq. (10) is never evaluated. The only explicit geometric term in the action, αT^n with n≈1.95, scales under the standard Weitzenböck FLRW torsion as H^{2n}, i.e., a^{-3n}, not a^{-3}. This is a direct internal inconsistency rather than a question of external consensus. I considered whether the missing MCMC details or the circular presentation of fitted parameters as predictions were the most load-bearing concern; both are serious, but they are secondary to the physical mechanism. If the torsion term does not scale as cold dark matter, the entire interpretation collapses regardless of how carefully the analysis were described. The concrete test above would settle the issue by producing the background equations that the paper omits. Therefore the REJECT verdict is appropriate and should remain unchanged.","tokens_in":9382,"tokens_out":4718,"duration_ms":61323,"concrete_test":"Insert the flat FLRW tetrad e^A_μ=diag(1,a,a,a) into Eq. (9) with F=R+αT^n, evaluate the 00 component using T=-6H^2, and solve the resulting background equations for H(a) in a matter-only universe. Then compute the effective torsion energy density ρ_T(a) from the torsion terms. If ρ_T(a) does not scale as a^{-3} when n=1.95, the central geometric-DM claim is falsified; if the paper cannot produce this calculation at all, the claim is unsupported. This single check would settle whether the quoted best-fit n is compatible with the claimed CDM-like scaling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing condition is the Sec. III statement that the torsion contribution in an FLRW background behaves like a pressureless dust component with density scaling as a^{-3}. The paper's conclusion in Sec. VII, that the torsion-based Myrzakulov F(R,T) gravity offers an observationally viable geometric alternative to particle dark matter, depends entirely on this scaling. Yet the paper never demonstrates it: the FLRW tetrad is never inserted into the field equations Eq. (9), no modified Friedmann equations are written down, and no explicit ρ_eff(a) is computed. Using the standard teleparallel result T=-6H^2, which follows from the definitions in Sec. II, the action F=R+αT^n in Eq. (11) gives a leading torsion contribution scaling as H^{2n}. In a matter-dominated background H^2∝a^{-3}, so αT^n scales as a^{-3n}, which for the fitted best-fit n=1.95 is a^{-5.85}, not a^{-3}. Unless an unusual cancellation in the unwritten Friedmann equations changes this, the geometric CDM mechanism fails for the paper's own best-fit parameters. This is an internal consistency problem, not merely a disagreement with the standard cosmological picture. The absence of any likelihood definition, dataset-specific model, or MCMC chain diagnostics further makes the observational claim unverifiable, but the scaling gap is the logically prior issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9725,"tokens_out":6177,"duration_ms":78593,"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":[{"comment":"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.","section":"Sec. III; Eqs. (10)-(11)"},{"comment":"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.","section":"Sec. V; Eq. (12), Table II"},{"comment":"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.","section":"Secs. III and VI; Figs. 1-2"},{"comment":"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.","section":"Sec. VI"},{"comment":"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.","section":"Secs. V-VI"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Eq. (12)"},{"comment":"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.","section":"Figs. 3-5"},{"comment":"References [22] and [28] are duplicates, as are [25] and [29]; the reference list should be consolidated and checked for consistency.","section":"References"},{"comment":"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.","section":"Eq. (11)"},{"comment":"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.","section":"Sec. V; Table I"}],"recommendation":"reject","confidential_remarks":"For the editor: the manuscript is heavily self-referential (refs. [6], [8]-[10], [16]-[19] are the authors' own work), and the novelty relative to those papers is not clearly articulated. More importantly, the core derivation is absent and the reported numerical analysis cannot be checked from the information given. I do not see a narrow revision path within the manuscript's scope: the central a^{-3} scaling claim needs to be derived or the model needs to be reformulated, and the entire observational section needs to be rebuilt with a defined likelihood and reproducible chains. I would not invite a revision unless the authors can supply the missing Friedmann equations and the complete analysis pipeline."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper has the shape of a research article but not the substance. The action F=R+αT^n is a two-parameter special case of the authors' own earlier Myrzakulov gravity work; the genuinely new component is supposed to be the multi-dataset MCMC fit, and that component is absent. No likelihood is defined, no sampler is named, no chains or convergence diagnostics are shown, and no code or data are provided. Table II is the entire empirical payload.\n\nWhat the paper does do reasonably: it clearly explains the vielbein setup, states field equations, and honestly flags the local Lorentz invariance issue in pure tetrad f(T) formulations. The list of datasets (SPARC, Planck, DES, KiDS, BAO, Pantheon+) is sensible for the intended test. The discussion of gravitational wave signatures is speculative but appropriately labeled as future work.\n\nThe soft spots are load-bearing. The central claim in Sec. III—that the torsion term behaves as pressureless dust scaling like a^-3 in FLRW—is never derived. The FLRW tetrad is never inserted into Eq. (9); no modified Friedmann equations appear; no ρ_eff(a) is computed. Under the standard teleparallel relation T=-6H^2 and matter domination H^2∝a^-3, the term αT^n scales as a^{-3n}; with the paper's own best fit n=1.95 that is a^{-5.85}, not a^{-3}. To rescue the claim you would need an unusual cancellation in the unwritten Friedmann equations, and the paper gives no hint of one. This is an internal consistency problem, not just a disagreement with ΛCDM.\n\nThere is also a circularity problem. The parameters α and n are fitted to Planck/DES/KiDS data, and then the resulting Ωm, H0, σ8 are presented as the model's 'predictions' or as 'consistent with' those same datasets. That is fitting presented as confirmation, and it runs through Secs. VI and VII. The conclusion's claim of an 'observationally viable' alternative rests entirely on that circle and on the unproved scaling.\n\nWho is this for? Someone tracking modified gravity overclaims might read it, but it will not be usable as a reference. The math is not developed enough to check, and the data analysis is not present. I would not cite it. It does deserve a serious referee, though: the scaling issue and the missing derivation are exactly the kind of thing a careful referee should document, and a high-profile claim in a popular area warrants formal review rather than a silent desk reject. Recommendation: send to review, and expect a substantial revision or, more likely, a rejection.","headline":"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.","tokens_in":10253,"tokens_out":3002,"would_cite":false,"duration_ms":31832,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Torsion can mimic dark matter without new particles, this gravity model claims.","keywords":["dark matter","torsion gravity","teleparallel gravity","F(R,T) gravity","vielbein formalism","Weitzenböck spacetime","cosmological parameter constraints","modified gravity"],"falsifier":"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.","tokens_in":9147,"feed_emoji":"🌌","tokens_out":7035,"duration_ms":79547,"temperature":0.7,"pith_summary":"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.","feed_headline":"Torsion can mimic dark matter without new particles","feed_subtitle":"A torsion-based gravity fit to galaxy rotation, CMB, and lensing data needs no dark matter particles.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Introduces the Myrzakulov $F(R,T)$ gravity framework that this paper extends to the vielbein formulation.","marker":"[6]"},{"why":"Prior work by the authors deriving the vielbein formalism in Weitzenböck spacetime used here.","marker":"[8]"},{"why":"Defines $f(R,T)$ gravity with $T$ as the trace of the energy-momentum tensor, the interpretation this paper explicitly departs from.","marker":"[7]"},{"why":"Provides the $f(T)$ teleparallel gravity and cosmology baseline that the torsion approach extends.","marker":"[11]"},{"why":"Supplies the SPARC galaxy rotation curves used to constrain the model at galactic scales.","marker":"[32]"},{"why":"Supplies Planck 2018 CMB parameters that anchor the cosmological fit.","marker":"[33]"},{"why":"Provides DES weak-lensing and clustering data constraining structure growth.","marker":"[34]"},{"why":"Provides KiDS-1000 cosmic shear measurements anchoring late-time lensing constraints.","marker":"[35]"}],"fun_headline_variants":["Torsion mimics dark matter without new particles","Geometric dark matter: torsion fits galaxy and cosmic data","No dark particles needed: torsion explains rotation curves","Torsion gravity fits data without dark matter particles","F(R,T) torsion: an alternative to dark matter and ΛCDM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Torsion mimics dark matter without new particles","Geometric dark matter: torsion fits galaxy and cosmic data","No dark particles needed: torsion explains rotation curves","Torsion gravity fits data without dark matter particles","F(R,T) torsion: an alternative to dark matter and ΛCDM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000208,"raw_usage":{"total_tokens":1373,"prompt_tokens":881,"completion_tokens":492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":497,"completion_tokens_details":{"reasoning_tokens":426}},"tokens_in":497,"tokens_out":492,"duration_ms":5675,"temperature":1.0,"reasoning_tokens":426,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T12:50:28.929756+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Einstein–Gauss–Bonnet–Myrzakulov gravity fromR+ F(T, G),","cited_arxiv_id":null,"evidence_quote":"Provides the $f(T)$ teleparallel gravity and cosmology baseline that the torsion approach extends."},{"cited_title":"Windhorst et al., Nature Astronomy7, 384 (2023)","cited_arxiv_id":null,"evidence_quote":"Supplies the SPARC galaxy rotation curves used to constrain the model at galactic scales."},{"cited_title":"SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves,","cited_arxiv_id":null,"evidence_quote":"Supplies Planck 2018 CMB parameters that anchor the cosmological fit."}],"review_version":1}