{"id":"7b56e357-a748-4466-9f60-fa0fc2957c8f","arxiv_id":"2411.12097","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The RGGR scale-dependent gravity parameter nu is constrained to |nu| of order 10^{-5}, consistent with LambdaCDM and unable to resolve the H0 or sigma8 tensions.","lead":"This paper tests a modified gravity model where Newton's constant and the cosmological constant vary with scale only in cosmological perturbations, keeping the background expansion identical to standard cosmology. Using Planck, supernova, BAO, and redshift-space distortion data, the authors find the model's one new parameter is consistent with zero, so it does not resolve the Hubble or sigma8 tensions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported constraint |ν|≲10^{-5} is not supported by Table 1: the joint 2σ interval is ν=5.8×10^{-5}±1.7×10^{-4}, i.e. [-1.1×10^{-4}, 2.3×10^{-4}]; the text and the reader's summary overstate the bound by an order of magnitude.","rationale":"The reader's weakest_assumption (scale-setting, W=-2ψ, constant ν) is a legitimate model-dependence caveat, but it is not an internal error: the paper consistently limits its conclusions to 'the RGGR, as implemented here' and explicitly says the framework 'unless further generalized, cannot address current cosmological issues'. The more immediate, checkable defect is the mismatch between the reported 2σ error (1.7×10^{-4}) and both the paper's conclusion text ('|ν|≲10^{-5}') and the reader's strongest_claim ('±1.7×10^{-5}'). This is an internal inconsistency in the central quantitative claim. The inconsistency does not overturn the main qualitative conclusion—that the model cannot resolve the H0 or σ8 tensions—because even the corrected upper bound (2.3×10^{-4}) is far below the values that would produce percent-level changes (see Fig. 1, where ν=±0.01 is required for visible CMB effects). Therefore the CONDITIONAL verdict remains appropriate, but the conditions should include correcting the reported bound and releasing the chains or code to verify the interval. Agreement with the reader is partial: the scale-setting point is valid and complementary, but the strongest factual issue is the error-bar misreport.","tokens_in":19038,"tokens_out":16468,"duration_ms":171329,"concrete_test":"Recompute the credible interval from Table 1: the joint row gives 2σ bounds ν = 5.815×10^{-5} +0.00017/−0.00017, so the 95% interval is [-1.1×10^{-4}, 2.3×10^{-4}]. Test three things: (1) verify that the table's error is in the same units as the central value (unitless), so the error is 1.7×10^{-4}; (2) check whether the conclusion '|ν|≲10^{-5}' is consistent with an upper bound of 2.3×10^{-4}; it is not; (3) confirm consistency with zero using the corrected 1σ error: 5.8×10^{-5}/8.5×10^{-5} = 0.68σ, so 'within 1σ' holds only with the corrected error, not with the reader's quoted 1.7×10^{-5} at 2σ. If the table notation instead meant 1.7×10^{-5}, the authors should show the corresponding MCMC chains to verify; otherwise the text should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is the magnitude of the RGGR parameter ν. Section 6 states that the data 'allowed us to constrain the value of ν to |ν| ≲ 10−5'. However, Table 1 (CMB+BAO+SNIa+RSD) reports ν = 5.815×10^{-5} +0.00017/−0.00017 at 2σ. The quoted 2σ errors are 1.7×10^{-4}, not 1.7×10^{-5}; the 95% interval is approximately [−1.1×10^{-4}, 2.3×10^{-4}], so |ν| can be as large as 2.3×10^{-4}. The text's '|ν|≲10^{-5}' overstates the constraint by more than a factor of 20. The reader's strongest_claim repeats this: '(5.8 ± 1.7) × 10^{-5} (2 sigma)' is internally inconsistent—with a 2σ error of 1.7×10^{-5}, zero would be 6.8σ away, not within 1σ. The correct reading is ν = (5.8 ± 8.5)×10^{-5} at 1σ (or ±17×10^{-5} at 2σ), which is consistent with ΛCDM. The conclusion that the model cannot resolve the H0 or σ8 tensions is likely unaffected, because even the 2σ upper bound 2.3×10^{-4} gives sub-percent parameter shifts, but the quantitative headline in the paper's conclusions is wrong and must be corrected.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper tests a specific action-based implementation of renormalization-group-improved gravity (RGGR) in cosmology. In the model, the gravitational constant G and the cosmological constant Λ depend on two RG scales introduced through Lagrange multipliers; the first scale is set by the Newtonian potential perturbation through W = -2ψ (Eqs. 13-16), so the background cosmology is exactly ΛCDM while the linear perturbations acquire extra terms controlled by a single parameter ν, with ν = 0 recovering GR. The authors derive the modified scalar perturbation equations (25)-(33), give analytic solutions for the matter era (Eqs. 35-45) and for the CMB acoustic monopole (Eqs. 51-53), implement the system in a modified version of CLASS, and run MontePython MCMC against Planck 2018 (TT-TEEE+lensing), Pantheon SNIa, BOSS DR12 BAO, and RSD data. Table 1 reports ν = 8.4×10^-5 ± 1.8×10^-4 (CMB only) and ν = 5.8×10^-5 ± 1.7×10^-4 (joint) at the quoted 2σ level, i.e., consistent with ΛCDM, and the authors conclude that this model cannot resolve the H0 or σ8 tensions and is disfavored relative to ΛCDM by Occam's razor.","tokens_in":19513,"tokens_out":22237,"duration_ms":213807,"significance":"If correct, the paper provides a clean null result for this class of infrared-RG modified gravity: the CMB acoustic-peak structure together with joint distance and growth data confines the running parameter to |ν| ≲ 2×10^-4 at 2σ (taking Table 1 at face value), far too small to produce measurable changes in growth or expansion, and it overturns the earlier suggestion that this framework could alleviate the growth tension through RSD flexibility. The main qualitative conclusion is robust and sensible, and the paper is honest in reporting a negative result. The strengths are the fully action-based construction of the scale dependence, the closed-form analytic approximation of the ν-induced acoustic distortion (Eq. 52), the use of standard public data with a well-established pipeline and convergence checks, and the explicit acknowledgment that the claim is scoped to the adopted scale setting. The evident caveat is that the tight bound applies to the W = -2ψ scale identification inherited from Refs. [21, 27]; other scale-setting prescriptions are not constrained by this analysis, a point the paper itself concedes by saying 'as implemented here'.","major_comments":[{"comment":"The central quantitative claim is not supported by the reported numbers. Section 6 states that the data 'allowed us to constrain the value of ν to |ν| ≲ 10−5', and the Introduction repeats that the value is 'of the order of 10−5'. However, Table 1 (joint CMB+BAO+SNIa+RSD) reports ν = 5.815×10^-5 with 2σ uncertainties +0.00017/−0.00017, i.e., ±1.7×10^-4, corresponding to a 95% interval of roughly [−1.1×10^-4, 2.3×10^-4]. The correct statement is |ν| ≲ 2.3×10^-4 at 2σ, or ν = (5.8 ± 8.5)×10^-5 at 1σ, which is within 0.7σ of zero; the bound in the text overstates the constraint by more than an order of magnitude and must be corrected. In addition, the caption of Table 1 says the limits are '2σ CL', yet the ΛCDM CMB-only value H0 = 67.26 ± 0.54 coincides numerically with the published Planck 2018 1σ value (67.36 ± 0.54 for TT,TE,EE+lowE), which suggests the quoted intervals may actually be 68% limits; the confidence-level convention must be verified and stated consistently, since the claim of compatibility 'within the 1σ confidence level' in Section 5.2 depends on it. The qualitative conclusion that the model does not resolve the tensions survives either reading, because even the 2σ upper bound produces sub-percent parameter shifts, but the headline constraint must be restated.","section":"Section 6, Table 1"},{"comment":"The treatment of the logarithmic mode in the CDM initial conditions is delicate and under-specified. Equation (68) defines f(η) = 3ν ∫ ψ d ln η, and Eq. (83) gives δc containing the term 6νψ0 ln(η/η0); the text then states: 'In our numerical analysis we consider η ∼ η0, therefore, logarithmic term is canceled.' Because Eq. (32) contains the source term −6Hνψ, the Boltzmann integration regenerates a logarithmic contribution as the solution evolves away from the initial time, so the cancellation can only be a choice of the constant of integration, not an elimination of the mode. Since this contribution is first order in ν, which is exactly the order of the effect being constrained, the authors should specify how the CLASS implementation treats this term (whether the initial conditions contain the log and whether the source term is integrated consistently), and should demonstrate that the ν posterior is insensitive to the initial integration time and to η0. This is a corrigible but load-bearing point, and the paper's own text flags it as an assumption rather than a derivation.","section":"Appendix A, Eqs. (32), (68), (83)"},{"comment":"The modified CLASS code is not released. The paper states that the key equations are implemented in a 'modified version of the Boltzmann solver code CLASS' and cites line numbers (perturbations.c, lines 6500 and 9128), but no code or patch is provided. The central claim of the paper is a posterior distribution generated by this code, and the analytic equations alone do not pin down the delicate implementation choices discussed above, such as the handling of the logarithmic CDM mode and the choice of initial conditions. I request that the code or a patch be made publicly available as supplementary material at the revision stage so that the numerical result is reproducible.","section":"Section 5.2"}],"minor_comments":[{"comment":"Equation (44) contains a double minus sign and a missing prime: the friction term is written as 'Hδb' instead of 'Hδb′', and '− −4πG0' should be a single minus sign; the equation should read δb'' + Hδb′ − [4πG0/(1−ν)]a²(εcδc + εbδb) = 0.","section":"Eq. (44)"},{"comment":"The term ln(√3x/k) in the definition of K(x) is not dimensionally consistent as written, since √3x/k = √3rs has units of length; the argument of the logarithm should be a dimensionless ratio, and the reference scale should be specified.","section":"Eq. (53)"},{"comment":"There are two typos: 'instroducing' should be 'introducing' in the text after Eq. (53), and 'strenght' should be 'strength' in the sentence defining ν below Eq. (16).","section":"Section 4 and near Eq. (16)"},{"comment":"The sentence 'we consider a total of seven cosmological parameters' is inconsistent with the footnote that adds the SN Ia absolute magnitude and high-ℓ CMB nuisance parameters; the sentence should distinguish the seven cosmological parameters from the additional nuisance parameters.","section":"Section 5.2"},{"comment":"The simplifying assumption that only CDM contributes to the background trace T (neglecting baryons) is asserted to be harmless; a one-line estimate of the fractional effect, which is of order νΩb/Ωm ≈ 0.2ν, would make this statement precise.","section":"Section 3, text after Eq. (31)"},{"comment":"The red/orange distinction between the ΛCDM and RGGR contours is hard to discern in the printed rendering; distinct line styles or a zoomed inset would improve readability.","section":"Figure 2"},{"comment":"Once the bound on ν is corrected, the conclusions should explicitly repeat that the bound applies to the W = −2ψ scale-setting (Eqs. 13–16); the text is already carefully scoped ('as implemented here'), but restating the conditionality next to the corrected number would prevent over-generalization in citations.","section":"Section 6"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the most important issue is the order-of-magnitude discrepancy between the paper's headline bound |ν| ≲ 10^-5 and the actual 2σ interval from Table 1, which is |ν| ≲ 2.3×10^-4. This is the central quantitative claim and must be corrected before acceptance. I also suspect the '2σ CL' caption of Table 1 may be wrong, because several ΛCDM uncertainties (e.g., H0 = 67.26 ± 0.54 for CMB-only) coincide numerically with Planck 2018's published 1σ values; the authors should verify their confidence-level convention and likelihood configuration. The paper is an incremental but legitimate constraint study on the authors' own framework, with a largely negative message that is honestly reported; the fit otherwise looks standard, and the qualitative conclusions survive the numerical correction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid null result for a specific RG-improved gravity model, but the paper's own summary of its main constraint is wrong by more than an order of magnitude. Referee time is warranted, not to kill the paper, but to force a correction and a code release.\n\nWhat's actually new: they take the two-scale RGGR framework from their own Ref. [27], implement the modified perturbation equations in CLASS, and run Planck 2018 + Pantheon + BAO + RSD. The result is that, for this scale-setting, ν is consistent with zero and the model does not resolve H0 or σ8 tensions. That is a legitimate, useful null result. The analytic approximation for the acoustic oscillations, Eq. (52), looks like a genuinely new and potentially handy tool for understanding why CMB peaks pin ν down so tightly. Credit where due: the paper does the heavy numerical lifting, uses standard public data, and states its main conclusion honestly — RG corrections here cannot dismiss the current tensions.\n\nThe soft spots, in order of size. First, the headline constraint. Section 6 says the data constrain ν to |ν| ≲ 10^-5, and the reader's summary repeated that. Table 1 says otherwise: the joint 2σ errors are ±1.7×10^-4, so the 95% interval is roughly [-1.1×10^-4, 2.3×10^-4]. The text overstates the bound by a factor of more than 20. The main conclusion survives — ν=0 is well inside the interval, and even the 2σ upper end gives sub-percent shifts — but the paper as written contains an internally inconsistent quantitative claim and the authors must fix it.\n\nSecond, the constraint is conditional on the scale-setting identification, W = -2ψ, inherited from Refs. [21, 27]. If the physical IR RG scale is tied to something else, say the Ricci scalar or an energy density, these bounds do not apply. The paper says this implicitly, but the conclusions are phrased in a more general way than the model actually warrants.\n\nThird, the modified CLASS code is not released, and the initial-condition branch selection in Appendix A is delicate. The paper points to line numbers in perturbations.c, which is helpful, but for a constraint paper the community standard is now to ship the code. I would make code release a condition of acceptance.\n\nThe citation pattern is self-referential but not abusive; this paper is a direct continuation of the authors' own framework, so citing it is expected.\n\nWho is this for: anyone testing scale-dependent or RG-modified gravity against CMB/LSS data, and anyone cataloging null results for tension solutions. It deserves a serious referee, mainly because the framework is well defined and the null result is worth having on record once the quantitative overstatement is corrected.","headline":"A well-executed null result for one specific RGGR model, but the paper's |ν|≲10^-5 headline is contradicted by its own Table 1 (the 2σ bound is ~2×10^-4); fix that and it earns referee time.","tokens_in":20046,"tokens_out":2565,"would_cite":true,"duration_ms":25180,"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":"This paper tests a gravity model whose constants G and Λ run with scale, and finds the single free parameter is pinned near one part in 100,000, leaving the Hubble and σ8 tensions unresolved.","keywords":["renormalization group improved gravity","scale-dependent gravitational constant","running cosmological constant","cosmological perturbations","CMB acoustic oscillations","Hubble tension","sigma8 tension","Markov Chain Monte Carlo"],"falsifier":"Build the same two-scale action with the primary scale tied to the local energy density or the Ricci scalar instead of psi, and fit it to the identical Planck, BAO, Pantheon, and RSD data: a model of that kind that evades the acoustic-peak constraint while shifting H0 by several km/s/Mpc would show that the paper's null result is a property of the scale choice rather than of renormalization-group running itself. Observationally, a CMB experiment with roughly an order-of-magnitude better acoustic-peak calibration than Planck, or growth measurements reaching sub-percent precision in f sigma8, could detect nu at the $10^{-5}$ level; a best-fit value deviating from zero by more than 2 $\\sigma$ would overturn the paper's central 'consistent with LambdaCDM' claim.","tokens_in":18798,"feed_emoji":"🌌","tokens_out":18724,"duration_ms":157969,"temperature":0.7,"pith_summary":"Quantum field theory suggests that physical constants run with energy scale, and extending that idea to gravity at cosmic scales motivates the model studied here: the gravitational constant $G$ and the cosmological constant $\\Lambda$ vary with scale at the level of perturbations, while the background expansion stays exactly general relativity. The paper builds this running into an action whose scale definitions are enforced by Lagrange multipliers, and derives the full perturbative equations; a single dimensionless parameter $\\nu$ carries every deviation from general relativity. Fitting Planck 2018 CMB, BAO, Pantheon supernovae, and redshift-space-distortion data, the joint analysis constrains $\\nu = 5.8 \\times 10^{-5}$ with a $2\\sigma$ uncertainty of $1.7 \\times 10^{-4}$, so the general-relativistic value $\\nu = 0$ is within $1\\sigma$. The CMB acoustic-peak structure does the constraining work: even $|\\nu|$ of order $10^{-2}$ visibly shifts the positions and amplitudes of the peaks, which is why CMB data alone already limit $\\nu$ to the $10^{-5}$ scale. The paper concludes that, in this two-scale form, the model cannot resolve the Hubble or $\\sigma_8$ tensions, although the action framework itself remains theoretically consistent.","feed_headline":"Data rule out running-G gravity as a fix for cosmic tensions","feed_subtitle":"A candidate fix for cosmology's biggest anomalies is pinned to a null result by Planck CMB data","key_machinery":"The load-bearing object is the effective action (1) with Lagrange multipliers $\\lambda_p$ that enforce the scale-setting conditions $\\mu_p = f_p(g,\\Psi,\\gamma)$ inside the integral, together with the specific two-scale identification: the first scale is set by $W = U^\\alpha U^\\beta(g_{\\alpha\\beta} - \\gamma_{\\alpha\\beta}) = -2\\psi$ in the Newtonian gauge, and the second scale is tied to the background value of the trace $T$. Expanding $G(\\mu_1) = G_0(1 - 2\\nu\\psi)$ to first order in $W$ with a single constant $\\nu$, and fixing $\\Lambda$ accordingly, converts the action into a concrete set of $\\nu$-corrected perturbation equations: the slip $\\phi/\\psi = 1 - 2\\nu$, a corrected Poisson equation, and a dark-matter continuity equation with source term $-6H\\nu\\psi$. The analytic solutions $\\psi \\propto \\eta^{\\bar\\nu}$ with $\\bar\\nu \\approx (6/5)\\nu$, and $\\delta_c \\propto a^{1+\\bar\\nu/2}$, show how a small $\\nu$ amplifies or suppresses potentials and growth. The mechanism that ultimately decides the model's fate is the damped, forced harmonic oscillator for the CMB monopole $\\Theta_0$: through $\\phi$ and $\\psi$, the forcing term acquires $\\nu$-dependence that shifts acoustic-peak positions and amplitudes, and Planck-scale data convert that sensitivity into the $10^{-5}$ bound.","core_discovery":"The central claim is a null result expressed as a tight constraint. In the two-scale, action-based RGGR model (renormalization-group improved general relativity), all running is carried by $\\nu$, defined through $G_0 G^{-1}(W) = 1 + \\nu W$ with $W = -2\\psi$, the Newtonian potential perturbation, while $\\Lambda$ is tied to the background trace of the energy-momentum tensor. The background equations are identical to general relativity, and only the perturbation sector changes: there is a gravitational slip $\\phi/\\psi = 1 - 2\\nu$, a source term $-6H\\nu\\psi$ in the cold-dark-matter continuity equation, and a slowly growing potential mode $\\psi \\propto \\eta^{(6/5)\\nu}$ that also alters structure growth, $\\delta_c \\propto a^{1+3\\nu/5}$, for positive $\\nu$. The joint CMB+BAO+SN+RSD fit returns $\\nu = 5.8 \\times 10^{-5}$ with $2\\sigma$ error $1.7 \\times 10^{-4}$, i.e., agreement with $\\Lambda$CDM within $1\\sigma$; the largest $2\\sigma$ shift in $\\sigma_8$ is below $0.5\\%$ and shifts in $H_0$ are below $1\\%$. The paper concludes that, in this implementation, infrared renormalization-group running of $G$ and $\\Lambda$ is consistent with the standard model's predictions and does not relieve either of its two main tensions.","pith_inferences":["The null result is conditional on the scale choice $W = -2\\psi$; a differently scaled variant with the running tied to energy density could in principle move $H_0$ or $\\sigma_8$ while leaving the CMB peaks intact, and the same action formalism makes that variant directly testable with the same datasets.","The analytic growth law $\\delta_c \\propto a^{1+3\\nu/5}$ implies that even a $\\nu$ at the current bound leaves a sub-percent imprint on growth data, so next-generation surveys could tighten the constraint by an order of magnitude or detect a nonzero value.","Because the model changes only perturbation-level observables, geometric probes such as BAO peak positions and supernova distances are blind to it; this illustrates that 'background-preserving' modified-gravity models must be tested with clustering and CMB-anisotropy data rather than distance measurements alone.","The $\\nu$-induced slip between $\\phi$ and $\\psi$ persists at late times even without anisotropic stress, so a future cosmological measurement of the slip through lensing and dynamics could probe the same parameter from an independent direction."],"forward_implications":["The two-scale RGGR model with linear-in-$\\psi$ running is observationally indistinguishable from $\\Lambda$CDM at current precision, with $\\nu$ consistent with zero within $1\\sigma$.","CMB acoustic-peak structure dominates the constraint; RSD data alone leave $\\nu$ almost unconstrained, and earlier hints of a negative $\\nu$ from growth data do not survive the joint analysis.","The model slightly enlarges the uncertainties on $n_s$, $H_0$, and $\\sigma_8$, but every shift relative to $\\Lambda$CDM stays below $1\\%$, so neither the Hubble nor the $\\sigma_8$ tension is alleviated.","Any model in this class that modifies the gravitational slip or the dark-matter conservation equation around recombination faces the same tight acoustic-peak bounds.","Since the running is forced to be tiny, the framework's phenomenological value would have to come from further generalization, such as different scale settings or additional running scales."],"supporting_citations":[{"why":"The two-scale, action-based RGGR framework from which the perturbative equations and the present analysis are taken.","marker":"[27]"},{"why":"Introduced the RGGR scale-setting at the level of the Newtonian potential perturbation, on which the identification W = -2psi is built.","marker":"[21]"},{"why":"Showed how to promote the scale-setting to the action via Lagrange multipliers, the step that the cosmological framework extends.","marker":"[29]"},{"why":"Supplies the Planck 2018 CMB and lensing likelihoods that dominate the constraint on nu.","marker":"[44]"},{"why":"Provides the Pantheon type Ia supernova sample used in the joint fit.","marker":"[45]"},{"why":"Supplies the 6dF Galaxy Survey BAO measurement used in the joint fit.","marker":"[30]"},{"why":"Supplies the BOSS DR12 BAO measurements used in the joint fit.","marker":"[31]"},{"why":"Provides the RSD growth-rate dataset and the fiducial-model correction procedure that the likelihood adopts.","marker":"[54]"},{"why":"The numerical Boltzmann solver that the authors modify with the RGGR perturbation equations and initial conditions to compute spectra.","marker":"[48]"},{"why":"The MCMC sampler used for the Bayesian parameter estimation and convergence checks.","marker":"[49]"}],"fun_headline_variants":["Null result: scale-dependent G won't fix Hubble tension","Running-G gravity: no relief for cosmic tensions","RG gravity stays consistent with ΛCDM, not tensions","Data rule out running-G as cosmic tension cure","Action-based RG gravity: same tensions, no solution"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The constraint rests on identifying the infrared renormalization-group scale with the Newtonian potential perturbation (W = -2psi) and expanding G and Lambda linearly in that quantity with a single constant nu; if the physical scale were set by a different quantity, or if nu itself ran with scale, the derived perturbation equations and the tight CMB bound would not apply.","fun_headline_variants_meta":{"raw":{"variants":["Null result: scale-dependent G won't fix Hubble tension","Running-G gravity: no relief for cosmic tensions","RG gravity stays consistent with ΛCDM, not tensions","Data rule out running-G as cosmic tension cure","Action-based RG gravity: same tensions, no solution"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000216,"raw_usage":{"total_tokens":1513,"prompt_tokens":1108,"completion_tokens":405,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":724,"completion_tokens_details":{"reasoning_tokens":329}},"tokens_in":724,"tokens_out":405,"duration_ms":4403,"temperature":1.0,"reasoning_tokens":329,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:54:45.602249+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build the same two-scale action with the primary scale tied to the local energy density or the Ricci scalar instead of psi, and fit it to the identical Planck, BAO, Pantheon, and RSD data: a model of that kind that evades the acoustic-peak constraint while shifting H0 by several km/s/Mpc would show that the paper's null result is a property of the scale choice rather than of renormalization-group running itself. Observationally, a CMB experiment with roughly an order-of-magnitude better acoustic-peak calibration than Planck, or growth measurements reaching sub-percent precision in f sigma8, could detect nu at the $10^{-5}$ level; a best-fit value deviating from zero by more than 2 $\\sigma$ would overturn the paper's central 'consistent with LambdaCDM' claim.","supporting_citations":[{"cited_title":"Bertini, Wiliam S","cited_arxiv_id":null,"evidence_quote":"The two-scale, action-based RGGR framework from which the perturbative equations and the present analysis are taken."},{"cited_title":"Rodrigues, Patricio S","cited_arxiv_id":null,"evidence_quote":"Introduced the RGGR scale-setting at the level of the Newtonian potential perturbation, on which the identification W = -2psi is built."},{"cited_title":"Rodrigues, Bertrand Chauvineau, and Oliver F","cited_arxiv_id":null,"evidence_quote":"Showed how to promote the scale-setting to the action via Lagrange multipliers, the step that the cosmological framework extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Pantheon type Ia supernova sample used in the joint fit."},{"cited_title":"The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes","cited_arxiv_id":null,"evidence_quote":"The numerical Boltzmann solver that the authors modify with the RGGR perturbation equations and initial conditions to compute spectra."}],"review_version":1}