{"id":"85d6bda0-e792-47c8-940e-4f0404851b6c","arxiv_id":"2501.14908","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"An f(T,T) gravity model with a fitted equation of state matches cosmic expansion data, giving H0=68.04, beta=0.14, gamma=0.96 and an accelerating late universe.","lead":"This paper tests a modified gravity model by fitting it to supernova and galaxy data, and reports that it can match the observed accelerating expansion. It is a routine consistency check, and several headline numbers are direct consequences of the assumed formula.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The effective-EoS ansatz in Sec. III is exactly the ΛCDM total EoS, so the fit does not independently test the f(T,T) coupling; with β consistent with zero and no baseline comparison, the derived q0, zt, and ω0 are not independent findings.","rationale":"The reader's weakest_assumption is the effective EoS ansatz, and my independent check identifies the same point as the most load-bearing issue. The central claim is that the f(T,T)=T+βT model is viable on the basis of the H(z)+Pantheon+ fit. For that claim to be a genuine test of the gravity theory, the fitted expansion history must be sensitive to the theory's field equations rather than being imposed by the assumed EoS. The ansatz ω(z) = -3/[γ(1+z)^3+3] is precisely the total EoS of ΛCDM; plugging it into Eq. (15) effectively selects the LCDM Hubble rate, with β=0 giving Eq. (19). The reported β is consistent with zero, and the derived q0, zt, and ω0 are analytic functions of the ansatz and the fitted parameters. Therefore the background fit cannot discriminate the f(T,T) modification from ΛCDM. I verified that the ODE integration leading to Eq. (18) is internally consistent, so this is not a claim of algebraic error. The missing pieces are a β=0/ΛCDM comparison, error propagation on derived parameters, and a perturbation-level stability check. The reader's conditional verdict is appropriate: the issues are fixable with standard statistical and perturbation analyses, but as presented the central claim is not established. Hence my recommendation is UNCHANGED.","tokens_in":13071,"tokens_out":15256,"duration_ms":147000,"concrete_test":"Re-run the MCMC analysis on the same H(z)+Pantheon+ data with β fixed to 0 (Eq. 19, the model's ΛCDM limit) and compute Δχ² or the Bayes factor against the free-β model. If Δχ² < 2 and the evidence does not favor β ≠ 0, the data provide no support for the f(T,T) coupling, and the paper's viability claim reduces to the statement that an LCDM-like EoS ansatz fits the data. As a secondary check, propagate the MCMC chains through Eqs. (18) and (21) to produce posterior distributions for q0 and zt; if these posteriors are broad enough to include the ΛCDM values, the reported point values are not precise model predictions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The derivation of Eq. (18) from the field equations and the adopted ansatz is algebraically consistent. The load-bearing problem is that the ansatz ω(z) = -3/[γ(1+z)^3+3], introduced in Sec. III to close the system, is exactly the total equation of state of ΛCDM with Ω_m/Ω_Λ = γ/3. Inserting this ansatz into Eq. (15) fixes the Hubble rate to the LCDM-like form of Eq. (18), and for β=0 it reduces to Eq. (19), the standard ΛCDM H(z). The data therefore constrain the parameters of a presupposed LCDM expansion history, rather than testing whether f(T,T)=T+βT modifies gravity. The fit itself confirms this: β = 0.14 ± 0.17 is consistent with zero, so the joint data do not require the β coupling. The headline quantities q0 = -0.51, zt = 0.57, and ω0 = -0.76 are analytic functions of the ansatz and the fitted β and γ; they carry no independent information about f(T,T) gravity. The paper also gives no error bars on q0, zt, or ω0, no likelihood comparison with the β=0/ΛCDM limit, and no perturbation-level stability test; the statement that positive ρ 'reinforces stability' is not a stability analysis. Without these, the central viability claim is unsupported: the exercise shows that an LCDM-like EoS ansatz fits the background data within the f(T,T) field equations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the cosmological viability of f(T, T) gravity with the linear form f(T, T) = T + βT in a flat FLRW universe. To close the field equations, the authors adopt an effective equation-of-state parameter ω(z) = −3/[γ(1+z)^3+3], derive the Hubble parameter H(z) in Eq. (18), and fit the model to a joint H(z)+Pantheon+ dataset using MCMC. They report best-fit parameters H0 = 68.04 ± 0.64, β = 0.14 ± 0.17, and γ = 0.96^{+0.38}_{−0.69}, and then compute q0 = −0.51, zt = 0.57, ω0 = −0.76, and a positive energy density, concluding that the f(T, T) model is a viable framework for cosmic acceleration.","tokens_in":13427,"tokens_out":5450,"duration_ms":75059,"significance":"If the central claim were supported, the paper would provide useful observational constraints on a specific f(T, T) model. The algebraic derivation of H(z) from the field equations and the adopted ansatz is internally consistent, and the MCMC analysis with a joint H(z)+Pantheon+ dataset is standard and reproducible in structure. These are genuine strengths. However, the significance is severely limited because the assumed effective equation of state is exactly the total equation of state of ΛCDM, so the fit essentially constrains the parameters of a preset ΛCDM-like expansion history rather than testing whether the β coupling is required. The reported values of q0, zt, and ω0 are deterministic functions of the ansatz and the fitted parameters, not independent cosmological findings, and no baseline comparison or perturbation analysis is provided. The paper is better viewed as a reconstruction exercise than as a test of f(T, T) gravity in its current form.","major_comments":[{"comment":"The assumed effective EoS, ω(z) = −3/[γ(1+z)^3+3], is exactly the total equation of state of a ΛCDM universe with Ω_m/Ω_Λ = γ/3. Since the total EoS determines H(z) in any FLRW background, Eq. (18) is a ΛCDM-like template, and for β = 0 Eq. (19) is precisely the ΛCDM Hubble rate. The data therefore constrain the parameters of a presupposed expansion history, not whether f(T, T) = T + βT modifies gravity. A concrete test would be a model-comparison statistic (Δχ², AIC, or BIC) against the β = 0 ΛCDM limit; with β = 0.14 ± 0.17 the data are fully consistent with β = 0, so the current analysis provides no evidence for the β coupling.","section":"Sec. III, Eqs. (15)–(19)"},{"comment":"The claims q0 = −0.51, zt = 0.57, and ω0 = −0.76 are not independent results: they are deterministic functions of the assumed ω(z) ansatz and the fitted β and γ. Moreover, no uncertainties are propagated to these derived quantities, so there is no statistical error bar on any of them. The authors should either propagate the MCMC posteriors to q0, zt, and ω0 and report their full marginalized distributions, or explicitly state that these are point estimates obtained from the best-fit parameters of an assumed template.","section":"Sec. V, Eq. (21) and Figs. 2–4"},{"comment":"The statement that a positive cosmic fluid energy density 'reinforces stability' is not a stability analysis. Positivity of ρ at the background level does not address ghost instabilities, gradient instabilities, or the growth of perturbations. The paper itself, in Sec. VI, acknowledges that 'the stability of the f(T, T) theory should be rigorously tested' and that future studies could 'detail stability analyses'; this directly contradicts the earlier stability claim. The stability statement should be removed or replaced with a genuine perturbation-level analysis.","section":"Sec. V, Fig. 3 and Sec. VI"},{"comment":"No goodness-of-fit or model-selection statistic is reported. The paper states that the best-fit parameters 'align well with current observational data,' but without a reduced χ², AIC, BIC, or a comparison to the ΛCDM limit, this statement is not quantitatively supported. Given that the model reduces to ΛCDM at β = 0, reporting such a comparison is essential for assessing whether the additional parameter β is justified by the data.","section":"Sec. IV"}],"minor_comments":[{"comment":"The partial derivatives f_T and f_{\\mathcal{T}} are both rendered with the same symbol in the text (e.g., 'fT = 1, fT = β'), which is confusing; the two derivatives should be distinguished with clear notation throughout.","section":"Sec. III, notation"},{"comment":"The abstract and Sec. V present q0, zt, and ω0 as headline findings without noting that they are fixed by the assumed form of ω(z) and the fitted parameters; a caveat should be added to avoid overinterpretation.","section":"Abstract and Sec. V"},{"comment":"The corner plot shows the 1σ and 2σ contours, but the text does not report the correlation coefficients between H0, β, and γ; reporting these would help the reader understand parameter degeneracies.","section":"Fig. 1"},{"comment":"The prior ranges are stated as H0 ∈ [50, 100], β ∈ [−1, 1], and γ ∈ [−1, 1], but the best-fit γ = 0.96 lies very close to the prior edge, and the posterior is asymmetric; the sensitivity of the results to the prior width should be discussed.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The circularity of the effective-EoS ansatz is a substantive issue: because ω(z) is exactly the ΛCDM total EoS, the fit cannot discriminate f(T, T) from ΛCDM on the background level, and β is consistent with zero. The algebraic work and MCMC implementation appear sound, but the interpretation needs substantial revision, including a baseline comparison, error propagation, and removal or support of the stability claim. If the authors are unwilling to reframe the paper as a reconstruction rather than a viability test, I would not support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a coherent but incremental parameter-estimation paper. The algebra checks out, the MCMC setup is standard, and the paper is honest about where its ingredients come from. But the central viability claim does not actually test f(T,T) gravity, because the ansatz chosen in Sec. III is exactly the ΛCDM total equation of state. Inserting it forces H(z) into an LCDM-like form; β is consistent with zero, and q0, zt, ω0 are analytic functions of the fitted γ and β. They are not independent findings.\n\nWhat is actually new: very little. The linear form f(T,T)=T+βT and the EoS ω(z)=-3/[γ(1+z)^3+3] are both taken from cited prior work. The contribution is applying this combination to H(z)+Pantheon+ with MCMC and reporting posterior contours. That is a legitimate extension within an established program, and the derivation from Eq. (15) to Eq. (18) is internally consistent. I also appreciate that they give the β=0 limit and note it corresponds to ΛCDM. The fit numbers are plausible.\n\nSoft spots, in order. (1) The circularity is load-bearing. The ω(z) ansatz fixes the expansion history to be LCDM-like before the data are used; the fit then constrains the parameters of a presupposed history. The fact that β=0.14±0.17 is consistent with zero is the clearest sign the joint dataset does not require the coupling. (2) The headline quantities q0, zt, and ω0 are quoted without uncertainties and are deterministic functions of the fitted parameters; presenting them as findings over-reads the model. (3) The statement that positive ρ 'reinforces stability' is not a stability analysis. Positive energy density is at most a necessary condition; stability in f(T,T) needs perturbation theory. The paper itself defers perturbative work to future study, which is the right place for it. (4) There is no model comparison with ΛCDM or a reported Δχ², so 'viability' is not quantified against the baseline. All of these are fixable, but fixing them changes the paper from a test of f(T,T) into a consistency check of LCDM-like expansion within f(T,T).\n\nWho this is for: readers working specifically on f(T,T) phenomenology who want a parameter scan of this linear model on current background data. It is not for a general cosmology audience and it does not deserve a headline slot. But it is a reproducible estimation exercise, not crackpot science.\n\nRecommendation: I would send it to a specialized gravity/cosmology journal and let a referee work it over. The referee should demand error bars on the derived quantities, an explicit ΛCDM baseline comparison, and language that does not overstate what the ansatz accomplishes. If the authors comply, the paper becomes a usable data point for that subfield.","headline":"A clean but largely circular f(T,T) background fit: the assumed effective EoS is exactly the ΛCDM total EoS, so the headline values are derived from the ansatz, not independent tests of modified gravity.","tokens_in":13934,"tokens_out":2058,"would_cite":false,"duration_ms":19207,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A linear torsion-matter coupling in $f(T,\\mathcal{T})$ gravity fits the joint cosmic-chronometer and Pantheon+ data, with an acceleration transition at $z\\approx 0.57$.","keywords":["f(T,T) gravity","torsion scalar","cosmic acceleration","dark energy","equation of state","MCMC","quintessence","observational cosmology"],"falsifier":"Fit the same two datasets to the $\\beta=0$ limit of the model with the same priors and compare the statistical evidence; if the evidence does not favor $\\beta\\neq 0$, the viability claim would lack support. Independently, replace the adopted $\\omega(z)$ with a model-agnostic two-parameter dark-energy form; if the best-fit $q_0$ and $z_t$ shift significantly from $-0.51$ and $0.57$, the headline numbers are artifacts of the assumed equation of state.","tokens_in":12888,"feed_emoji":"🔭","tokens_out":12643,"duration_ms":94071,"temperature":0.7,"pith_summary":"The paper aims to show that the minimal extension of teleparallel gravity with $f(T,\\mathcal{T}) = T + \\beta\\mathcal{T}$ stays viable against the main late-universe distance and expansion data. The authors close the field equations with an effective equation of state that depends on redshift, integrate to a closed-form Hubble law, and fit it to 31 cosmic-chronometer measurements plus 1701 Pantheon+ supernovae. Their best-fit parameters are $H_0 = 68.04 \\pm 0.64$, $\\beta = 0.14 \\pm 0.17$, and $\\gamma = 0.96^{+0.38}_{-0.69}$, from which they derive $q_0 = -0.51$, $z_t = 0.57$, and $\\omega_0 = -0.76$. A sympathetic reader would care because the model reproduces the observed deceleration-to-acceleration transition and a quintessence-like dark-energy equation of state without putting a cosmological constant into the action.","feed_headline":"Matter-coupled gravity model fits cosmic acceleration data","feed_subtitle":"Fit to 1,701 supernovae and 31 Hubble measurements, it gives H0≈68 and an acceleration transition at z≈0.57.","key_machinery":"The machinery is the linear functional form $f(T,\\mathcal{T}) = T + \\beta\\mathcal{T}$, where $T$ is the torsion scalar of teleparallel geometry and $\\mathcal{T}$ is the trace of the energy-momentum tensor, together with the redshift-dependent effective equation of state $\\omega(z) = -3/(\\gamma(z+1)^3+3)$ used to close the generalized Friedmann equations. This ansatz is what converts the field equations into a single first-order equation for $H(z)$, yielding the closed-form solution and the derived expressions for $q(z)$, $\\rho(z)$, and $\\omega(z)$ that are later compared with data. The same equation of state has the limiting behavior $\\omega \\to 0$ at high redshift (matter-like) and $\\omega \\to -1$ as $z \\to -1$ (cosmological-constant-like), which anchors the model's claim to describe both the matter era and late-time acceleration.","core_discovery":"On its own terms, the central discovery is that the linear model $f(T,\\mathcal{T}) = T + \\beta\\mathcal{T}$, together with the assumed effective equation of state $\\omega(z) = -3/(\\gamma(1+z)^3+3)$, produces a Hubble parameter of the closed form $H(z)=H_0\\left[\\frac{-12\\beta+(\\beta+2)\\gamma(1+z)^3+6}{-12\\beta+(\\beta+2)\\gamma+6}\\right]^{\\frac{2\\beta+3}{3\\beta+6}}$, and that this law fits the joint $H(z)$+Pantheon+ data with the quoted parameter values. The same solution gives $q_0=-0.51$, a transition redshift $z_t=0.57$, a current effective equation of state $\\omega_0=-0.76$, and a positive energy density at every redshift. The paper presents these as evidence that $f(T,\\mathcal{T})$ gravity can mimic late-time cosmic acceleration and act as a geometric alternative to dark energy.","pith_inferences":["A consequence the paper leaves implicit is that, because the assumed $\\omega(z)$ is exactly the total equation of state of a $\\Lambda$CDM background, the fitted $q_0$, $z_t$, and $\\omega_0$ are largely dictated by the ansatz; a truly independent test of $f(T,\\mathcal{T})$ gravity would need a reconstructed $\\omega(z)$ rather than the $\\Lambda$CDM one.","The $1\\sigma$ interval for $\\beta$ includes zero, so the current data do not require the torsion-matter coupling; a formal model comparison against the $\\beta=0$ limit would show whether the extra parameter is justified.","Re-running the same closed-form pipeline with a different two-parameter dark-energy equation of state would show whether the quoted parameter values are robust or an artifact of the $\\Lambda$CDM-shaped $\\omega(z)$.","The stability result reported is only for the homogeneous background energy density; perturbative stability and growth-rate data remain the open ground on which the model's viability must be decided."],"forward_implications":["A nonzero but small $\\beta$ is compatible with the joint dataset, so the matter-trace coupling does not spoil the successful late-time expansion history.","The derived transition redshift $z_t=0.57$ places the deceleration-to-acceleration crossover close to $\\Lambda$CDM expectations, which is what a viable dark-energy alternative must reproduce.","With $\\omega_0=-0.76$, the model's effective fluid sits in the quintessence regime rather than the phantom regime, so it avoids a $\\omega<-1$ singularity at the background level.","Because the energy density stays positive across the fitted redshift range, the homogeneous solution is free of the sign-flip pathologies that can appear in modified-gravity models.","If the claim is right, $f(T,\\mathcal{T})$ deserves perturbative stability and structure-formation tests, as the paper itself notes, since background fits alone do not establish full viability."],"supporting_citations":[{"why":"Introduces the $f(T,\\mathcal{T})$ gravity action and field equations used throughout.","marker":"[53]"},{"why":"Supplies the redshift-dependent effective equation of state that closes the field equations.","marker":"[59]"},{"why":"Provides the 31 cosmic-chronometer $H(z)$ measurements entering the joint likelihood.","marker":"[69]"},{"why":"Provides the 1701 Pantheon+ supernova distances and covariance treatment used in the fit.","marker":"[76]"},{"why":"Specifies the MCMC sampling method used to estimate the posterior distribution.","marker":"[66]"},{"why":"Shows the $\\beta=0$ limit reduces to a $\\Lambda$CDM-like Hubble law, the comparison baseline.","marker":"[65]"},{"why":"Supplies the quoted present deceleration parameter $q_0$ reference.","marker":"[85]"},{"why":"Provides Planck 2018 values for $\\omega_0$ and $q_0$ used as consistency checks.","marker":"[10]"}],"fun_headline_variants":["Torsion-matter gravity model passes cosmic acceleration tests","Matter-coupled torsion gravity fits H0=68 and z_t=0.57","f(T,𝒯) model yields quintessence-like acceleration","Best-fit f(T,𝒯) gravity: H0=68, transition at z=0.57"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the assumed pressure-to-density ratio of the cosmic fluid, $\\omega(z) = -3/(\\gamma(1+z)^3+3)$; since this is exactly the pressure-to-density ratio of a $\\Lambda$CDM universe, the derived expansion history and headline numbers are pre-shaped to look like $\\Lambda$CDM no matter what the $f(T,\\mathcal{T})$ extension does.","fun_headline_variants_meta":{"raw":{"variants":["Torsion-matter gravity model passes cosmic acceleration tests","Matter-coupled torsion gravity fits H0=68 and z_t=0.57","f(T,𝒯) model yields quintessence-like acceleration","Best-fit f(T,𝒯) gravity: H0=68, transition at z=0.57"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001402,"raw_usage":{"total_tokens":5755,"prompt_tokens":1116,"completion_tokens":4639,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":732,"completion_tokens_details":{"reasoning_tokens":4553}},"tokens_in":732,"tokens_out":4639,"duration_ms":31988,"temperature":1.0,"reasoning_tokens":4553,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:48:21.453634+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit the same two datasets to the $\\beta=0$ limit of the model with the same priors and compare the statistical evidence; if the evidence does not favor $\\beta\\neq 0$, the viability claim would lack support. Independently, replace the adopted $\\omega(z)$ with a model-agnostic two-parameter dark-energy form; if the best-fit $q_0$ and $z_t$ shift significantly from $-0.51$ and $0.57$, the headline numbers are artifacts of the assumed equation of state.","supporting_citations":[{"cited_title":"Harko et al., J","cited_arxiv_id":null,"evidence_quote":"Introduces the $f(T,\\mathcal{T})$ gravity action and field equations used throughout."},{"cited_title":"Pace and J","cited_arxiv_id":null,"evidence_quote":"Supplies the redshift-dependent effective equation of state that closes the field equations."},{"cited_title":"Moresco, Mon","cited_arxiv_id":null,"evidence_quote":"Provides the 31 cosmic-chronometer $H(z)$ measurements entering the joint likelihood."},{"cited_title":"Mukherjee, Mon","cited_arxiv_id":null,"evidence_quote":"Specifies the MCMC sampling method used to estimate the posterior distribution."},{"cited_title":"Basilakos, Phys","cited_arxiv_id":null,"evidence_quote":"Shows the $\\beta=0$ limit reduces to a $\\Lambda$CDM-like Hubble law, the comparison baseline."},{"cited_title":"Myrzakulov et al., Eur","cited_arxiv_id":null,"evidence_quote":"Supplies the quoted present deceleration parameter $q_0$ reference."},{"cited_title":"Aghanim et al., Astron","cited_arxiv_id":null,"evidence_quote":"Provides Planck 2018 values for $\\omega_0$ and $q_0$ used as consistency checks."}],"review_version":1}