{"id":"c7d5a8e3-9e74-4dfe-b94e-6e5b5afdf2d9","arxiv_id":"2608.02175","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A combined fit of galaxy-growth, supernova, and CMB data finds at most a weak 2.2σ hint for scale-dependent suppression of structure growth, with an inconclusive Bayes factor.","lead":"The authors test whether the growth of large cosmic structures is weaker on very large scales by adding one adjustable 'scale-dependent' knob to the standard cosmological model and fitting it to galaxy, supernova, and cosmic-microwave-background data. They report a mild 2.2-sigma hint for such suppression, but the same analysis says the standard model and this extension are statistically indistinguishable.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Fixed-scale assumption is the linchpin: k=0.1 h/Mpc is asserted, not demonstrated; because ξ∝1/k² and A rescales with k², the 2.2σ evidence is untested against the k choice.","rationale":"The paper's headline is a 2.2σ indication for A>0, but A is not a physical observable: it multiplies ξ(k) ∝ 1/k², so the numerical value of A is set by the arbitrary choice k=0.1 h/Mpc. The only defense offered is a single sentence asserting that other reasonable k choices do not affect the results, with no supporting scan, figure, or table. The reader's weakest assumption identifies exactly this gap. This is load-bearing because if the posterior for B or the derived significance shifts when k moves within the linear regime, the advertised 2.2σ is not a property of the data but of the chosen coordinate in parameter space. I also note the fσ8 compilation is not a set of single-k measurements; treating all points as k=0.1 is an additional effective-scale assumption that compounds the problem. The concrete k-scan would settle this directly: if Δχ²_min and the significance of the dimensionless suppression Aξ are stable, the concern does not land; if they wander, the central claim is premature. The paper's own Bayesian evidence is already inconclusive, so the fixed-k robustness is the most economical way to test whether the frequentist-style 2.2σ deserves weight. The reader's CONDITIONAL verdict already reflects this; my assessment does not change it.","tokens_in":17362,"tokens_out":13310,"duration_ms":121537,"concrete_test":"Re-run the full fσ8+CC+SN+CMB MCMC at k=0.02, 0.05, 0.1, 0.15, 0.2 h/Mpc with the same priors and data. Report for each: A, B, Δχ²_min, and the profile-likelihood significance of the physical suppression Aξ(k=0.1, a=1). If Δχ² and the significance vary by <~1σ, the fixed-k choice is benign; if the significance drops below ~1σ or the B posterior piles at the 0 boundary, the 2.2σ evidence is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—2.2σ evidence for A>0—depends on the choice k=0.1 h/Mpc in ξ(t,k) (Eq. 5). The paper fixes this value just after Eq. (12) and asserts 'other reasonable choices of k have no appreciable effect' without showing a k-scan. Because A multiplies ξ, the same physical suppression at a different k is obtained by A∝1/k²; the quoted A=4425±2000 is therefore not a scale-invariant statement. More importantly, the parameter B is defined with a fixed 10^4 normalization, so a flat prior on B is not invariant under a change in k. At k=0.05, the best-fit A should be roughly 1100, which moves B from 0.36 to ~0.10; whether the posterior error shrinks proportionally is exactly what the missing k-scan would show. If the significance is driven by the arbitrary normalization/prior, the '2.2σ evidence' is an artifact. In addition, the 35 fσ8(z) points are not single-k measurements: each RSD value is an average over a survey-dependent k-window. A scale-dependent model predicts fσ8(k,z), not a single fσ8(z), so comparing the model at one k to all data points requires an effective-k assumption that is not tested. The paper's own Bayes factor (ln B_ij=-0.87) is inconclusive, reinforcing that the 2.2σ claim is the only pillar of the headline; the fixed-k choice is the weakest part of that pillar.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a phenomenological scale-dependent modification of the linear growth of matter perturbations, replacing the standard gravitational coupling G with G_eff(t,k)=G/[1+A ξ(t,k)], where ξ=3 H_0^2 Ω_m0/(a c^2 k^2). Using CLASS and MontePython, the authors jointly fit this model to 35 uncorrelated fσ8(z) measurements, cosmic chronometer H(z) data, PantheonPlus supernovae, and Planck 2018 CMB data. In the full dataset combination they report A=4425±2000 (B=0.36^{+0.14}_{-0.12}), interpreted as a 2.2σ preference for scale-dependent suppression of growth, while also reporting that the Bayesian evidence is inconclusive (ln B_ij=-0.87) and that the model does not alleviate the S8 or H0 tensions. The paper emphasizes that the suppression is stronger at z≳0.5 and that the model remains consistent with Planck values of S8 and H0.","tokens_in":17829,"tokens_out":2707,"duration_ms":23040,"significance":"If the central 2.2σ result were robust, it would be an interesting hint of scale-dependent gravitational behavior on linear scales, with implications for modified gravity and for interpretations of fσ8 measurements. The paper has several strengths: it uses public, well-established Boltzmann and MCMC tools; it gives a clear χ² breakdown per dataset; and it honestly reports the inconclusive Bayes factor, which tempers the headline significance. However, the central claim currently rests on a fixed, unvalidated choice of k, a one-sided prior on the amplitude, and a non-independent comparison with Planck-derived S8 and H0. With the evidence as presented, the paper is more a proof-of-concept constraint than a robust detection. The question of whether the claimed 2.2σ is scale-choice dependent is directly testable and should be resolved before the result is used as evidence for new physics.","major_comments":[{"comment":"The fixed choice k=0.1 h/Mpc is load-bearing for the central result. Because ξ∝1/k², the amplitude A and the posterior for B are not invariant under a change of k: the same physical suppression at k=0.05 h/Mpc corresponds to A~1100 and B~0.10, not B=0.36. The sentence 'Other reasonable choices of k have no appreciable effect on our results' is not a substitute for a k-scan. Please show the marginalized posterior of A (or B) and the resulting significance for at least k=0.05, 0.07, 0.1, 0.15, 0.2 h/Mpc, and state whether the 2.2σ indication persists across that range.","section":"Section 2, Eq. (5) and text after Eq. (12)"},{"comment":"The 2.2σ is a one-sided posterior probability for A>0 from a flat prior on B∈[0,3], not a model-comparison significance. The paper's own Bayes factor, ln B_ij=-0.87, is described as inconclusive under Kass & Raftery. This internal tension should be addressed directly: either the headline should be framed as 'a mild one-sided preference within a fixed parametrization' or the paper should justify why the Bayesian evidence is being discounted. Reporting a two-sided posterior probability or ΔBIC/ΔAIC would clarify what the data actually support.","section":"Eq. (9) and Table 3"},{"comment":"The agreement of S8=0.831±0.011 and H0=67.38±0.52 with Planck values is presented as validation, but Planck CMB data are included in the same joint fit. This agreement is therefore not independent and cannot be used to argue that the model preserves the Planck picture. Please rephrase this as internal consistency of the joint fit, or perform a fit excluding CMB data if the goal is an independent cross-check.","section":"Section 3, S8 and H0 consistency discussion"},{"comment":"The model predicts fσ8(k,z), but the 35 fσ8 measurements are reported as single values per redshift, each averaged over a survey-dependent k-window. Comparing the model at k=0.1 h/Mpc to all points assumes that every RSD measurement is effectively at that single wavenumber. This assumption is not tested. The paper should at least discuss the typical effective k of the surveys in the compilation and ideally marginalize over or propagate the k-window uncertainty.","section":"Section 2.1 and Figure 2"}],"minor_comments":[{"comment":"The abstract says 'evidence for scale-dependent growth at 2.2σ' while Section 3 repeatedly uses 'indication' and 'hint'. Please harmonize the language to match the statistical strength and the inconclusive Bayes factor.","section":"Abstract"},{"comment":"The footnote explaining the 10^4 normalization says ξ is 'typically of order 10^-5', but the units in Eq. (5) are not explicitly stated. Please state that k is in h/Mpc and that ξ is dimensionless with the conventions used, to avoid confusion.","section":"Eq. (9)"},{"comment":"The Δχ²_min values are useful, but the total Δχ²_min=-6.04 is compared with a Bayesian ln B_ij=-0.87 without giving the number of degrees of freedom or the effective penalty. A brief explanation of why the χ² improvement does not translate into positive evidence would help the reader.","section":"Section 3, Table 3"},{"comment":"The caption says 'dark blue curves' for fσ8 only, but the figure legend uses multiple colors. Please ensure the color description matches the actual plot, and consider labeling curves directly for accessibility.","section":"Figure 1"},{"comment":"Some references are incomplete or inconsistently formatted (e.g., 'Dent et al. 2009' is cited with arXiv numbers but some entries lack page numbers or journal identifiers). A final reference cleanup is needed.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is honest in its reporting, but the central 2.2σ claim is currently underdetermined by the fixed k choice and the one-sided prior. The missing k-scan is a straightforward addition and should be made mandatory. If the k-scan shows stability, the result would be a modest but interesting hint; if not, the paper should be reframed as an upper-limit study. I also recommend asking the authors to clarify the non-independence of the Planck consistency checks, since the current wording overstates the significance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent model-fitting paper whose advertised headline — 2.2σ evidence for scale-dependent growth — is the only pillar for new physics, and that pillar is shakier than the abstract suggests. The actual contribution is the first joint CC+SN+fσ8+CMB constraint on the amplitude A of the Dent et al. scale-dependent growth parametrization. Without CMB data the analysis gives upper limits; adding Planck shifts the fit to a nonzero A=4425±2000, i.e. B=0.36+0.14−0.12, a 2.2σ preference, with total Δχ²_min=−6.04. The paper is transparent about the main caveats: it reports its own Bayes factor (ln B=−0.87) as inconclusive and explicitly says ΛCDM remains fully consistent. That transparency is the strongest thing about it.\n\nWhat is done well: standard MCMC with CLASS and MontePython, a reasonably clean uncorrelated fσ8 compilation, a per-dataset breakdown of Δχ², a Bayesian model comparison, and appropriately cautious language in the body. The upper limits on A without CMB are useful and the authors do not oversell the result in the text. The problems are real but mostly interpretive. First, k=0.1 h/Mpc is fixed with a bare assertion after Eq. (12) that other reasonable choices have no appreciable effect, and no k-scan is shown. Since ξ∝1/k², the amplitude A effectively rescales as k², so the quoted central value and the posterior on B are not scale-invariant statements; the flat prior on B is also not invariant under a change of k. Second, the 35 fσ8 points are not single-k measurements — each is an average over a survey-dependent k-window — so comparing a single-k model to all points requires an effective-k assumption that is not tested. Third, the S8 consistency with Planck is not an independent validation because Planck is in the same joint fit. Fourth, the B≥0 prior is one-sided, which makes a 2.2σ preference less clean than a two-sided detection would be, and the Bayes factor is inconclusive. None of these break the paper as a constraints exercise, but they do mean the \"evidence\" framing in the abstract is doing more work than the analysis supports.\n\nWho is this for? People constraining modified-growth parametrizations and anyone who wants current upper limits on A. It deserves a serious referee: a good referee would ask for a k-scan, an effective-k treatment, and a cleaner separation between constraints and evidence in the abstract. I would send it out.","headline":"Read this as a constraints paper, not as evidence for new physics: the first joint CC+SN+fσ8+CMB constraint on the Dent et al. scale-dependent amplitude is useful and honestly analyzed, but the 2.2σ hint rests on a fixed, untested k choice and the paper's own Bayes factor is inconclusive.","tokens_in":18358,"tokens_out":2111,"would_cite":true,"duration_ms":18773,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the growth of cosmic structures is mildly scale-dependent, finding a 2.2σ preference for a non-zero scale-dependent correction to the growth equation when combining fσ8, cosmic chronometer, supernova, and CMB data, whi","keywords":["cosmology","large-scale structure","scale-dependent growth","modified gravity","fσ8","structure growth suppression","MCMC","ΛCDM"],"falsifier":"Repeat the MCMC analysis at k=0.05 and k=0.2 h/Mpc (a k-scan) and check whether the posterior for A or B shifts by more than the reported uncertainties, or whether the 2.2σ preference for A>0 disappears; a strong k-dependence of the inferred amplitude would show the result is not robust to the fixed scale. A direct test would be measuring fσ8 in two or more independent k-bins within the same redshift range to look for the predicted (1+z)/k² suppression pattern.","tokens_in":17261,"feed_emoji":"🔭","tokens_out":3199,"duration_ms":86144,"temperature":0.7,"pith_summary":"This paper tests whether the apparent suppression in the growth rate of cosmic structures, seen in fσ8 data, can be explained by a scale-dependent modification of the growth equation. It introduces an effective gravitational coupling that weakens gravity on large scales and fits the model to a combination of growth-rate, expansion-history, and CMB data. The central result is a 2.2σ indication for a non-zero scale-dependent amplitude when CMB data are included, implying suppressed clustering at large scales and earlier times. Without CMB, the data give only upper limits, and the standard ΛCDM model remains fully consistent; the scale-dependent model fits the growth data somewhat better but Bayesian evidence is inconclusive. A sympathetic reader would see this as a quantitative, cautious hint that linear structure growth may depart from strict scale independence, worth testing with future surveys.","feed_headline":"Cosmic growth shows 2.2-sigma hint of scale dependence","feed_subtitle":"Combining growth, expansion, and CMB data favors suppressed clustering on large scales; without CMB only limits emerge.","key_machinery":"The central object is a scale-dependent effective gravitational coupling, Geff(t,k)=G/(1+ξ(t,k)), inserted into the linear growth equation for matter density perturbations. The correction is ξ=3H0²Ωm0/(a c² k²), so it grows as (1+z)/k², vanishing at small scales and low redshifts. The analysis fixes k=0.1 h/Mpc and samples an amplitude parameter B=ln(1+A/10⁴), which enforces A≥0 and reduces to ΛCDM at B=0. This machinery converts a growth-rate anomaly into a constraint on large-scale gravitational weakening, and the k-dependence is what makes the model distinguishable from standard growth.","core_discovery":"The paper claims that linear matter clustering at scales near k=0.1 h/Mpc is plausibly suppressed relative to the GR/ΛCDM prediction, with an effective gravitational coupling Geff=G/(1+Aξ) where ξ∝(1+z)/k². Using a joint MCMC analysis of 35 uncorrelated fσ8 measurements, cosmic chronometer H(z) data, Pantheon+ supernovae, and CMB power spectra and lensing, the inferred amplitude A=4425±2000 (equivalently B=0.36+0.14−0.12) gives a 2.2σ preference for a non-zero scale-dependent term. The suppression is stronger during the matter-dominated era than in the dark-energy-dominated epoch, and the derived S8=0.831±0.011 matches the CMB-inferred value without exacerbating either the S8 or H0 tensions.","pith_inferences":["The 2.2σ evidence appears only when CMB data are included; without it, the same parametrization yields only upper limits. This suggests the signal is driven by the CMB's tight anchoring of Ωm,0 and σ8,0, and could be sensitive to CMB calibration or systematics rather than a genuine scale-dependent growth effect.","Because the correction scales as 1/k², the inferred amplitude A is inversely tied to the assumed wavenumber k=0.1 h/Mpc. A natural extension is to treat k as a free parameter or fit the growth rate in several k-bins; if A shifts with k as 1/k², the current parametrization may be absorbing a scale-mismatch rather than a physical effect.","A scale-dependent weakening of gravity on large scales would also affect weak lensing shear, CMB lensing, and void statistics on comparable scales; cross-correlating these probes with fσ8 in matched k-bins would provide an independent test of the claim.","The inconclusive Bayes factor (|lnB|<1) suggests the extra parameter is not yet justified on model-selection grounds; future redshift-space distortion surveys with finer k-resolution and lower systematics are needed to push the evidence beyond the current threshold."],"forward_implications":["If the 2.2σ signal is real, linear matter clustering at large scales (k≈0.1 h/Mpc) is suppressed relative to GR/ΛCDM, equivalent to an effective gravitational coupling below G at early times and large scales.","The suppression is stronger in the matter-dominated era than in the dark-energy-dominated epoch, so high-redshift growth measurements are the most sensitive probes of the effect.","The model keeps S8 and H0 consistent with CMB-inferred values, meaning a scale-dependent growth term does not worsen the current cosmological tensions.","The non-CMB dataset combinations yield upper limits on A (A≲6700–9900 at 95% CL), providing a quantitative bound on possible large-scale deviations at the O(10%) level in clustering strength.","Future surveys probing wider k-ranges and higher redshifts should distinguish the scale-dependent growth model from ΛCDM more decisively than current data."],"fun_headline_variants":["2.2σ evidence for scale-dependent cosmic structure growth","Large-scale structure growth shows 2.2σ anomaly","Cosmic growth suppression stronger in matter era, 2.2σ","Scale-dependent gravity fits fσ8 data without worsening tensions"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The analysis fixes the comoving wavenumber to k=0.1 h/Mpc for all fσ8 measurements and asserts, without showing a scan, that other reasonable choices of k have no appreciable effect—yet since the correction ξ is proportional to 1/k², the inferred amplitude A and the 2.2σ evidence are tied to that assumed scale.","fun_headline_variants_meta":{"raw":{"variants":["2.2σ evidence for scale-dependent cosmic structure growth","Large-scale structure growth shows 2.2σ anomaly","Cosmic growth suppression stronger in matter era, 2.2σ","Scale-dependent gravity fits fσ8 data without worsening tensions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000661,"raw_usage":{"total_tokens":2881,"prompt_tokens":788,"completion_tokens":2093,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":532,"completion_tokens_details":{"reasoning_tokens":2023}},"tokens_in":532,"tokens_out":2093,"duration_ms":11485,"temperature":1.0,"reasoning_tokens":2023,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T12:53:01.787224+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the MCMC analysis at k=0.05 and k=0.2 h/Mpc (a k-scan) and check whether the posterior for A or B shifts by more than the reported uncertainties, or whether the 2.2σ preference for A>0 disappears; a strong k-dependence of the inferred amplitude would show the result is not robust to the fixed scale. A direct test would be measuring fσ8 in two or more independent k-bins within the same redshift range to look for the predicted (1+z)/k² suppression pattern.","supporting_citations":[],"review_version":1}