{"id":"575dfa60-328a-49f8-8285-d5d4e21546d6","arxiv_id":"2411.11923","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"An f(T,T) gravity model fitted to Pantheon+, BAO, and cosmic chronometer data yields a range of H0 posteriors that track the input priors, and predicts a growth rate about 9-11% below ΛCDM for two data combinations.","lead":"This paper constrains an f(T,T) modified gravity model using supernova, cosmic chronometer, and baryon acoustic oscillation data, with and without SH0ES Hubble constant priors. It finds that the fitted Hubble constant shifts with the priors, and that some data combinations give a lower matter-growth rate than the standard cosmological model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The σ8-alleviation result rests on the assumed quasi-static growth equation (34) with G_eff from Eq. (35); because the f(T,T) perturbation system is never derived, the reported 9–11% fσ8 deficit is not established.","rationale":"The paper's background fit results are mostly prior-driven, and the H0-range observation is not surprising. Its only physically nontrivial assertion is the σ8-tension statement, and that assertion depends on substituting an effective Newton constant into the standard growth equation without deriving the perturbation theory of the trace-coupled action. The reader's weakest_assumption identifies exactly this step. An external citation [49] supplies a derivation in the literature, so the concern is not that the formula is fabricated, but that the present paper neither reproduces nor states the conditions under which Eq. (35) is valid; the quasi-static, dust-only, sub-horizon limit is assumed silently. Since the paper gives no RSD likelihood either, the quantitative 9–11% claim is a comparison of two theoretical curves, not a demonstrated resolution of the σ8 tension. This supports the reader's CONDITIONAL verdict: the claim would be creditable if the growth equation were derived and the fσ8 predictions checked against data, but as written the evidence is insufficient. No additional objection that would require a stronger verdict is apparent.","tokens_in":29316,"tokens_out":18122,"duration_ms":175921,"concrete_test":"Derive the scalar perturbation equations for action (6) in the quasi-static sub-horizon limit, retaining δT and pressure terms, and compare the resulting effective gravitational coupling with Eq. (35) at the best-fit parameters of Tables I and III; if the two disagree, recompute fσ8(0) with the correct equations and, if possible, a full RSD likelihood to see whether the deficit survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central nontrivial claim—that the f(T,T) model eases the σ8 tension by predicting lower fσ8(0)—is carried entirely by Eqs. (34)–(35). Section V writes the standard sub-horizon quasi-static growth equation and inserts P(a)=(1+f_T/2)/(1+f_T) as 'demonstrated', citing Refs. [46,49], but it never derives these equations from action (6) or field equations (7). Because the action couples to the matter trace T, the perturbed field equations contain δT, pressure, and f_{TT}/f_{TT} gradient terms; whether they cancel or are negligible in the quasi-static limit must be shown explicitly. The failure mode is concrete: if the full scalar-perturbation system yields a modified Poisson equation with additional k^2/a^2 or δT contributions, the effective G entering Eq. (36) is not Eq. (35), and the quoted 9% and 11% reductions in Fig. 3b are unsupported. In addition, those percentages compare the model curves to a ΛCDM curve, not to the RSD fσ8 measurements mentioned in the caption, so the conclusion overstates what the analysis actually demonstrates.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies late-time cosmology in f(T,T) gravity with the specific form f(T,T)=αT^n+Λ, using MCMC likelihood analyses of cosmic chronometer, Pantheon+ (with and without SH0ES), and BAO data, with R21 and TRGB H0 priors. It reports constraints on H0, Ωm0, n, and the nuisance parameter M for thirteen dataset combinations, computes χ²_min, AIC, and BIC relative to ΛCDM, and solves numerically the linear matter-growth equation to produce fσ8(z) curves. The central claims are that the dataset combinations yield a range of H0 values that could help with the Hubble tension, and that the model predicts fσ8 about 9–11% below ΛCDM, potentially easing the σ8 tension.","tokens_in":29639,"tokens_out":9398,"duration_ms":93194,"significance":"If the growth calculation is correct, the paper provides a useful set of late-time constraints for a specific f(T,T) model and a candidate mechanism for lowering fσ8 without invoking new matter physics. The MCMC analysis covers a wide range of data combinations with full CC and BAO covariance matrices, and the AIC/BIC comparison with ΛCDM is a useful consistency test. The model predicts a quintessence-like equation of state and a deceleration-to-acceleration transition consistent with observations. However, the two headline results are currently not established: the H0 range is mostly a reflection of the input priors, and the fσ8 reduction rests on an effective Newton constant that is asserted rather than derived from the theory's perturbation equations. These issues, together with internal errors in the model-comparison tables, limit the paper's impact until corrected.","major_comments":[{"comment":"The σ8-alleviation claim rests entirely on the adopted growth equation with P(a)=(1+f_T/2)/(1+f_T). The paper states that this \"can be demonstrated\" and cites Refs. [46,49], but it does not derive the quasi-static sub-horizon perturbation system from action (6) and field equations (7). Because f(T,T) couples to the matter trace, the perturbed equations generically contain δT, pressure, and scale-dependent gradient terms; their cancellation or suppression in the quasi-static limit must be shown explicitly. Without this, the reported 9% and 11% reductions of fσ8 are an assumption, not a derived prediction.","section":"Sec. V, Eqs. (34)–(35), Fig. 3b"},{"comment":"The caption states that the complete RSD fσ8 dataset of Ref. [93] is used, but the figure only superposes model and ΛCDM curves; no RSD likelihood, residuals, or χ² are reported. The claims in Sec. VII that the model \"could provide a better fit to large-scale structure observations\" and that the curves are \"approximately 9%\" and \"11% below ΛCDM\" are comparisons with ΛCDM only, not with the data. A quantitative fit to the RSD points is required to support the σ8-tension claim.","section":"Sec. V.A, Fig. 3b and Sec. VII"},{"comment":"The information criteria in Table II are internally inconsistent. For CC+PN++BAO+R21, AIC−χ²_min = 308, which would require k=154 parameters if AIC=χ²_min+2k, whereas all other rows in the same table give k=4; the value χ²_min=1524.96 is likely a typo for 1824.96. For CC+PN++R21, AIC=1798.52 with χ²_min=1780.52 gives k=9, while the model has four free parameters and the AIC should be 1788.52. These errors propagate into ΔAIC and ΔBIC and undermine the statistical comparison in Sec. IV.","section":"Table II"},{"comment":"The \"primary finding\" that different dataset combinations yield a range of H0 values, and that this \"could contribute to reducing the cosmic tension,\" is a restatement of the input priors rather than a model prediction. Adding the R21 prior or SH0ES points shifts H0 toward 73 km/s/Mpc by construction, and the normalization Λ=H0² after Eq. (33) makes H0 an input to the Lagrangian. To claim that the model reduces the H0 tension, the paper must demonstrate that the model, without such priors, produces a high H0 or reconciles early- and late-universe calibrations through an internal mechanism.","section":"Abstract and Sec. IV/VII"}],"minor_comments":[{"comment":"The conclusion contains \"CC+PAN+\" in place of \"CC+PN+\" in three places; this typo should be corrected.","section":"Sec. VII"},{"comment":"The R21 prior is quoted as H0=73.04±1.04 and attributed to Ref. [12], whose central value is 73.30±1.04; the label and value should be made consistent (R21 versus R22).","section":"Sec. III and Table I"},{"comment":"The MCMC analysis does not report chain lengths, burn-in, acceptance rates, or prior ranges; without these the numerical constraints in Tables I and III cannot be reproduced.","section":"Sec. III"},{"comment":"The sound-horizon calculation uses Ωb,0=0.02242 without specifying h; since this is Ωb h², the calculation needs the assumed h or a separate Ωb input to be unambiguous.","section":"Eq. (24)"},{"comment":"Equation (33) is an implicit equation for E(z), but the numerical root-finding method and branch selection used to solve it are not described.","section":"Eq. (33) and Sec. IV"},{"comment":"The text states σ(a)∼δm(a) with δm(a)≈a; this approximation should be justified in the context of Eq. (36), since the growth equation is being integrated numerically.","section":"Sec. V.A, Fig. 3a"}],"recommendation":"major_revision","confidential_remarks":"The paper is a serviceable but not highly novel MCMC constraints exercise. The two headline physical claims—H0-tension reduction and σ8-easing—are either prior-driven or depend on an unverified growth equation. My recommendation of major revision is driven by the need to derive Eq. (35) from the perturbation equations and to correct Table II; if the growth derivation cannot be supplied, the σ8 claims should be removed or explicitly framed as a test of an assumed formula. The paper is within the scope of a cosmology/gr-qc journal and the background constraints are potentially useful once the statistical tables are fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a parameter-estimation exercise for a known f(T,T) model, and the headline H0 result is just prior-following. The one nontrivial claim—easing the sigma8 tension—rests on a growth equation that is assumed rather than derived for this theory, so I wouldn't take that result to the bank. That said, the MCMC work is honest and reasonably thorough, and with some fixes it could be a usable contribution.\n\nWhat's actually new: the with/without SH0ES comparison on Pantheon+ in f(T,T) gravity, and the systematic scan over data combinations with H0 priors. The model itself is from ref [51] and the f(T) prior study is from Briffa et al. [57], so novelty is incremental. The background evolution and corner plots look like standard, careful work; the AIC/BIC machinery is the right tool.\n\nWhere it soft: first, the growth-rate section. Eqs. (34) and (35) are stated with a citation, but the paper never derives the effective Newton constant for f(T,T) with trace coupling. Since the action couples to T, the perturbed field equations will contain delta-T and pressure terms; it's not obvious they cancel in the quasi-static limit. If they don't, G_eff is not the simple P(a) used here, and the 9-11% f_sigma8 deficit is unsupported. Second, the statistics tables have visible internal inconsistencies: AIC = chi^2 + 2k with k=4 for CC+PN++R21 gives 1788.52, not 1798.52, and the chi^2=1524.96 for CC+PN++BAO+R21 looks like a typo for 1824.96. BIC values also don't match the stated formula with the actual sample sizes. These are fixable but need attention. Third, the sigma8 claim compares model curves to LCDM, not to the RSD measurements plotted in Fig. 3b; the paper doesn't compute a fit to those data, so 'better fit to LSS observations' overstates the evidence.\n\nWho this is for: readers working on modified-gravity constraints and the H0/sigma8 tension question will find the dataset scan useful as a reference. The central conclusions should be treated with caution until the perturbation system is properly sorted. I'd send it back for major revision rather than reject it out of hand; it's the kind of paper that can become solid once the growth equation is justified and the tables are corrected.","headline":"A routine MCMC scan of a known f(T,T) model whose H0 result follows the priors, and whose sigma8-easing claim rests on an underived growth equation; fixable, but not ready as is.","tokens_in":30183,"tokens_out":3575,"would_cite":false,"duration_ms":32570,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05"],"pacs":["04.50.Kd","98.80.Es"],"model":"deepseek-v4-flash","headline":"The paper argues that a trace-coupled torsion gravity model can produce Hubble-constant estimates on both sides of the cosmic tension while predicting slower matter growth, potentially easing both the H0 and σ8 tensions.","keywords":["f(T,T) gravity","teleparallel gravity","Hubble tension","sigma8 tension","H0 priors","supernova cosmology","baryon acoustic oscillations","matter growth fsigma8"],"falsifier":"A concrete decisive check would be to derive the full linear scalar perturbation equations for the action and see whether they reduce to the assumed sub-horizon growth equation with the simple effective coupling; if extra pressure or scale dependence appears, recomputing $f\\sigma_8$ with the correct coupling would show whether the predicted 9–11 percent deficit survives. A second, simpler check is a single joint MCMC fit to all datasets simultaneously: if no parameter choice yields an $H_0$ consistent with both the local and early-universe measurements, the claimed easing of the Hubble tension is not a simultaneous resolution.","tokens_in":29110,"feed_emoji":"🌌","tokens_out":11433,"duration_ms":106631,"temperature":0.7,"pith_summary":"The paper argues that the modified gravity model $f(T,\\mathcal{T})=\\alpha T^n\\mathcal{T}+\\Lambda$ can accommodate both sides of the Hubble-constant dispute and simultaneously predict less structure growth than the standard cosmological model. The authors fit the model to cosmic-chronometer, supernova (with and without local distance-ladder calibration), and baryon acoustic oscillation data, plus two external $H_0$ priors, using MCMC. Their fits produce $H_0$ values ranging from roughly 64.7 to 72.7 km/s/Mpc depending on which data and priors are used, with the local-calibrated supernova set pushing $H_0$ up near 73 and BAO pulling it down near 67. Solving the linear growth equation with the model's effective gravitational coupling gives $f\\sigma_8(0)$ values about 9–11 percent below $\\Lambda$CDM for two parameter choices, which would go in the direction of easing the $\\sigma_8$ tension. If the model is right, a single trace-coupled torsion theory could explain late-time acceleration while softening both major observational tensions in cosmology.","feed_headline":"Modified gravity model eases both cosmic tensions","feed_subtitle":"A trace-coupled teleparallel gravity model fits late-time acceleration and predicts 9–11 percent less structure growth.","key_machinery":"The load-bearing objects are the model Lagrangian $f(T,\\mathcal{T})=\\alpha T^n\\mathcal{T}+\\Lambda$, the implicit dimensionless Hubble equation $E^2(z)=(1+z)^3\\Omega_{m0}-\\frac16+(1-\\Omega_{m0}+\\frac16)(1+z)^3E^{2n}(z)$, and the effective gravitational coupling $P(a)=G_{\\rm eff}/G=(1+f_{\\mathcal{T}}/2)/(1+f_{\\mathcal{T}})$ that enters the linear growth equation $\\delta_m''+(2+H'/H)\\delta_m'-(3/2)(G_{\\rm eff}/G)\\Omega_m\\delta_m=0$. The trace-derivative $f_{\\mathcal{T}}$ is what carries the modification: it shifts the inferred expansion rate when different data sets are combined and simultaneously suppresses the growth of matter overdensities relative to $\\Lambda$CDM. The numerical evolution of $\\delta_m$ and the resulting weighted growth rate $f\\sigma_8(z)=f_\\delta(a)\\sigma(a)$ converts these couplings into the paper's headline predictions.","core_discovery":"The central claim is that in $f(T,\\mathcal{T})$ gravity with $f(T,\\mathcal{T})=\\alpha T^n\\mathcal{T}+\\Lambda$, different data combinations tune the model's parameters so that the inferred Hubble constant interpolates between early-Universe and late-Universe values: with the 1701-point supernova sample plus cosmic chronometers the best fit is about 66.4 km/s/Mpc, adding the local distance-ladder calibration raises it to about 72.5–72.7 km/s/Mpc, and adding BAO lowers it to 64.7–70.3 km/s/Mpc depending on priors. The paper also claims that the same model, through the effective Newton constant $P(a)=G_{\\rm eff}/G=(1+f_{\\mathcal{T}}/2)/(1+f_{\\mathcal{T}})$ entering the sub-horizon growth equation, yields a weighted growth rate $f\\sigma_8(0)$ about 9–11 percent lower than $\\Lambda$CDM for the parameter sets that include BAO, and it reproduces late-time background diagnostics (deceleration parameter, quintessence equation of state, matter-to-dark-energy transition, and the $Om(z)$ diagnostic) broadly consistent with observation. Because the model has no $\\Lambda$CDM limit, these results are presented as genuine modified-gravity alternatives rather than small perturbations of the standard model.","pith_inferences":["Going beyond the paper, a full derivation of the linear perturbation equations for this $f(T,\\mathcal{T})$ action is the natural decisive test; the coupling to the matter trace can introduce pressure and scale-dependent terms that the assumed quasi-static equation omits.","Going beyond the paper, the spread in $H_0$ across separate fits is evidence of parameter flexibility, not yet proof of a single model that fits all data simultaneously; a joint fit with all datasets and their covariances would be the sharper test of tension reduction.","Going beyond the paper, the model's growth prediction could be tested directly against the full redshift-space-distortion catalogue at multiple redshifts, since the two parameter sets that give the 9–11 percent deficit also carry a spread in $\\sigma_8$ (0.76–0.85) that affects the comparison.","Going beyond the paper, the same effective gravitational coupling could be probed in the nonlinear regime with N-body simulations, whose cluster-count and weak-lensing predictions would distinguish this model from $\\Lambda$CDM independently of linear growth."],"forward_implications":["If the central claim holds, $f(T,\\mathcal{T})$ gravity with this functional form is a viable late-time alternative to $\\Lambda$CDM that reproduces the accelerated expansion and passes AIC/BIC comparison for the supernova-plus-chronometer combinations.","The model's ability to return $H_0$ near 73 with local calibrations and near 67–69 with BAO means that future joint analyses simultaneously using all probes could either resolve or sharpen the Hubble tension depending on whether one global fit can match all data.","The predicted $f\\sigma_8$ deficit of roughly 9–11 percent relative to $\\Lambda$CDM at $z=0$, if confirmed by full perturbation theory, would bring the model in line with large-scale structure measurements that see weaker clustering than the early-Universe extrapolation.","Because the model has no $\\Lambda$CDM limit, improved distance-ladder and BAO measurements will eventually distinguish it from $\\Lambda$CDM through the shape of $H(z)$ and the growth rate, not just through overall $\\chi^2$.","The background diagnostics indicate quintessence-like evolution, so the model predicts specific redshift-dependent dark-energy behavior that future surveys can test."],"supporting_citations":[{"why":"Defines the $f(T,\\mathcal{T})$ action, field equations, and the effective Newton constant $P(a)$ that the growth analysis assumes.","marker":"[46]"},{"why":"Supplies the local distance-ladder supernova calibration and the $H_0=73.04\\pm1.04$ km/s/Mpc prior that drives the high-$H_0$ fits.","marker":"[12]"},{"why":"Supplies the TRGB distance-calibration prior of $H_0=69.8\\pm1.9$ km/s/Mpc used as the intermediate prior.","marker":"[14]"},{"why":"Provides the early-universe CMB parameters, the sound-horizon value, and the reference $\\Lambda$CDM parameters used for comparison.","marker":"[15]"},{"why":"Provides the supernova analysis and its with/without distance-ladder calibration variants that the paper compares.","marker":"[56]"},{"why":"Supplies the consensus BAO measurements included in the BAO chi-square term.","marker":"[5]"},{"why":"Supplies the redshift-space-distortion $f\\sigma_8$ data and the normalization convention used to compare growth rates and define the tension.","marker":"[93]"},{"why":"Provides the MCMC sampler used for all the parameter constraints.","marker":"[63]"}],"fun_headline_variants":["Teleparallel gravity tweaks Hubble constant, eases tension","f(T,𝒯) gravity fits supernovae and BAO to relieve Hubble tension","Modified gravity interpolates Hubble constant, easing cosmic tension","Teleparallel gravity with trace coupling eases H0 and growth tensions","Alternative gravity model may reduce cosmic tension using data combos"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the linear growth of matter clustering in this trace-coupled gravity is captured by the standard sub-horizon equation with a simple effective Newton constant; the paper does not derive the perturbation equations for the theory, so if pressure or scale-dependent corrections appear in a full derivation, the predicted drop in growth is unsupported.","fun_headline_variants_meta":{"raw":{"variants":["Teleparallel gravity tweaks Hubble constant, eases tension","f(T,𝒯) gravity fits supernovae and BAO to relieve Hubble tension","Modified gravity interpolates Hubble constant, easing cosmic tension","Teleparallel gravity with trace coupling eases H0 and growth tensions","Alternative gravity model may reduce cosmic tension using data combos"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00058,"raw_usage":{"total_tokens":2811,"prompt_tokens":1101,"completion_tokens":1710,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":717,"completion_tokens_details":{"reasoning_tokens":1621}},"tokens_in":717,"tokens_out":1710,"duration_ms":12815,"temperature":1.0,"reasoning_tokens":1621,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:41:45.145798+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete decisive check would be to derive the full linear scalar perturbation equations for the action and see whether they reduce to the assumed sub-horizon growth equation with the simple effective coupling; if extra pressure or scale dependence appears, recomputing $f\\sigma_8$ with the correct coupling would show whether the predicted 9–11 percent deficit survives. A second, simpler check is a single joint MCMC fit to all datasets simultaneously: if no parameter choice yields an $H_0$ consistent with both the local and early-universe measurements, the claimed easing of the Hubble tension is not a simultaneous resolution.","supporting_citations":[],"review_version":1}