{"id":"23d19df0-4edb-45af-b41e-6c5d46920296","arxiv_id":"2411.15619","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":22,"one_line_summary":"In generalized Rastall gravity, accretion of the CBDRM and CDMMA dark energy parameterizations increases the mass of a non-singular black hole over cosmic time, according to the authors' mass-redshift equations.","lead":"This paper calculates how the mass of a non-singular black hole changes as the universe expands, using two dark energy models inside a modified theory of gravity called generalized Rastall gravity. The authors fit model parameters to supernova, cosmic chronometer, and baryon acoustic oscillation data, then find that in both models the black hole gains mass over cosmic time and compare this with the standard Lambda-CDM universe.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq (33) makes the sign of dM/dt proportional to the unconstrained coefficient (λB0+B1); the paper never fixes B1, so the claimed mass increase is not a consequence of the fitted dark-energy parameters.","rationale":"The paper is a straightforward MCMC-constrained application of an accretion formula to two dark-energy parameterizations. The derivation of Eq (33) appears to follow the modified conservation law, but the sign of the mass flux is not fixed by the cosmological fit. Since B1 enters as an arbitrary integration constant and B0 depends on unspecified black-hole parameters, the mass-versus-redshift curves are not predictions from the constrained parameters alone. The reader's weakest_assumption correctly identified B1 as the decisive gap; I agree. The additional problems of posterior means outside their stated priors and the inconsistent treatment of λ=δ/R further weaken the analysis, but the B1 issue is the most load-bearing because it can invert the conclusion without changing any fitted parameter. This reinforces rejection, so no verdict adjustment is proposed.","tokens_in":21408,"tokens_out":5339,"duration_ms":49230,"concrete_test":"Recompute M(z) for CBDRM and CDMMA from Eqs (36)–(39) with the Table I parameters, repeating the integration with B1=−2λB0, B1=0, and B1=+λB0 while keeping all other inputs fixed. If M(z) decreases for any negative B1, the abstract's unconditional mass-increase claim fails. Additionally, the authors should state the values of a and b used to evaluate B0 and the boundary condition fixing B1; Figures 3–5 are not reproducible without them.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion follows from integrating \\dot M = 4π(λB0+B1)(ρ+p)M^2, Eq (33), into Eq (35). The factor (λB0+B1) multiplies the entire integrand in Eqs (36) and (38). The text after Eq (33) states that ρ+p>0 gives mass increase, but this is only true if λB0+B1>0. B1 is introduced in Eq (31) as an arbitrary integration constant with no value, prior, or boundary condition, while B0=(4f/r−2rf″) depends on the nonsingular metric (26), whose constants a and b are not specified for the accretion plots. The MCMC table constrains cosmological parameters, not B1 or a,b. Therefore, for identical fitted parameters one can choose B1 sufficiently negative to reverse the inequality and make M(z) decrease even though ρ+p>0 for the same dark-energy models. Figures 3–5 thus do not demonstrate the headline mass-increase claim. A secondary internal inconsistency is that Table I reports posterior means outside the stated priors (CBDRM λ=0.339±0.037 with prior [0,0.1] and ω1=1.756±0.017 with prior [0,0.1]; CDMMA λ=−0.082±0.004 with prior [0,0.1]), and λ and δ are treated as independent despite Eq (2) defining λ=δ/R; these reinforce, but are not needed for, the B1 objection.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies mass accretion onto a non-singular black hole in generalized Rastall gravity, using two dynamical dark-energy equation-of-state parameterizations (CBDRM and CDMMA). The authors first constrain the model parameters with MCMC analyses of Cosmic Chronometers, Pantheon+ SNe Ia, and DESI/DES BAO data, then derive a mass-redshift relation from the modified conservation equation and plot the black-hole mass evolution for both parameterizations and for ΛCDM. The central claim, stated in the abstract and repeated in the conclusions, is that accreting either of the two dark-energy parameterizations, with constrained parameters, increases the black-hole mass during cosmic evolution.","tokens_in":21874,"tokens_out":4283,"duration_ms":41168,"significance":"If the central claim were established, the paper would connect observational cosmological constraints to a specific prediction for black-hole mass evolution in a modified gravity theory, which is a potentially interesting cross-area result. The manuscript has some strengths: it uses public observational datasets, employs standard Bayesian tools (polyChord and GetDist), presents explicit posterior tables and statistical model comparisons, and writes the accretion equations in a transparent algebraic form. However, the main physical conclusion is not supported by the presented calculation. The sign of the mass change is controlled by an arbitrary integration constant, and the MCMC priors appear inconsistent with the reported posteriors. Because these issues directly affect the headline prediction, the paper's claim about the 'true nature of dark energy' from accretion is not established.","major_comments":[{"comment":"The sign of the mass accretion rate in Eq. (33), dM/dt = 4π(λB0+B1)(ρ+p)M^2, is proportional to the product (λB0+B1)(ρ+p). The text after Eq. (33) argues that ρ+p>0 implies mass increase, but that conclusion requires λB0+B1>0. The constant B1 is introduced in Eq. (31) as an arbitrary integration constant, and no value, prior, or boundary condition is specified for it anywhere in the paper. In addition, B0 = 4f(r)/r − 2r f''(r) depends on the metric function f(r) in Eq. (26), which contains the unspecified parameters a and b. Therefore the fitted MCMC parameters in Table I do not determine the sign or magnitude of the mass evolution. For the same fitted dark-energy parameters, one can choose B1 < −λB0 and obtain a decreasing mass for identical cosmological input. Consequently, Figures 3-5 and the abstract's claim of mass increase are not consequences of the constrained parameters.","section":"Section IV, Eqs. (31)-(35)"},{"comment":"Table I reports posterior means that lie outside the stated prior ranges: for CBDRM, λ = 0.339 ± 0.037 with prior [0, 0.1], ω1 = 1.756 ± 0.017 with prior [0, 0.1], and δ = 1.059 ± 0.540 with prior [0, 1]; for CDMMA, λ = −0.082 ± 0.004 with prior [0, 0.1]. With bounded uniform priors, a posterior distribution supported outside the prior box is impossible in a correctly implemented nested-sampling or MCMC run. This indicates either misreported priors or an error in the sampling procedure. Since the paper's stated novelty is parameter constraining, this inconsistency directly undermines the reliability of the constraints used in all subsequent accretion plots.","section":"Section III, Table I"},{"comment":"The generalized Rastall theory is defined with λ = δ/R in Eq. (2), but in Section III the parameters λ and δ are treated as independent free parameters with independent priors and independent posterior means (e.g., for CBDRM, λ = 0.339 ± 0.037 and δ = 1.059 ± 0.540). No constraint enforcing λ = δ/R appears in the analysis. Because λ and δ both enter the Hubble parameter expressions in Eqs. (17) and (21) and the accretion integrand in Eqs. (36) and (38), this internal inconsistency affects the quantitative results and should be resolved before the mass-accretion conclusion can be assessed.","section":"Section II, Eq. (2), and Section III, Table I"},{"comment":"Equation (34), which states (ρ+p) = −[(1−3ϵλ(1+ω(z)))/(3H(1−4ϵλ))] ρdot, is asserted without derivation. It does not follow directly from the generalized conservation law in Eq. (7); one would need additional assumptions relating Hdot, ρ, and ω(z). Since Eq. (35) is obtained by substituting Eq. (34) into Eq. (33), this missing derivation is a load-bearing step for the mass equation and for the plotted mass evolution. The authors should either provide the derivation or state the additional relation used.","section":"Section IV, Eq. (34)"}],"minor_comments":[{"comment":"Each of Figs. 3 and 4 appears to show two identical side-by-side panels. If these are duplicate panels, they should be removed; if they are meant to show different quantities or parameter choices, the panels should be labeled and the difference explained.","section":"Figures 3 and 4"},{"comment":"The axes in Figures 3-5 are not clearly labeled with units or normalization. Equation (35) gives M in terms of M0, but the plots show unlabeled values; the authors should state whether the plotted quantity is M/M0 and specify the values used for M0, a, b, and B1.","section":"Figures 3-5"},{"comment":"The phrase 'redial temporal component' should be 'radial temporal component'.","section":"Section IV, paragraph after Eq. (30)"},{"comment":"The title and abstract contain stylistic and typographical issues, including a missing space before the question mark in the title and several comma splices; a careful language edit is recommended.","section":"Abstract and title"}],"recommendation":"reject","confidential_remarks":"The paper uses public datasets and standard statistical tools, which is commendable, and the derivation of the accretion equations is presented explicitly. However, the central claim is not supported by the calculation: the sign of the mass change is set by an unconstrained integration constant, and the MCMC priors appear inconsistent with the reported posterior means. These are load-bearing issues that would require a reformulation of the paper's main physical conclusion rather than a minor revision. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe useful piece here is Section IV: they take the standard spherically symmetric accretion setup, adapt it to the non-conserved stress-energy of generalized Rastall gravity, and end up with explicit mass-redshift integrals for the CBDRM and CDMMA equation-of-state parameterizations (Eqs. 36 and 38). Those specialized formulas are not in the cited literature, and the MCMC work in Section III (CC + Pantheon + DESI BAO) is competent and standard. Credit is due for laying out the cosmological side carefully and for making the black hole metric and its properties explicit.\n\nThe problem is that the central claim does not follow from their own equations. Eq. (33) gives dM/dt = 4π(λB0+B1)(ρ+p)M^2. The sign of dM/dt is controlled by (λB0+B1), not by (ρ+p) alone. B1 is introduced in Eq. (31) as an arbitrary integration constant; no value, prior, or boundary condition is ever assigned to it. B0 = 4f/r − 2rf'' depends on the metric function (26), whose constants a and b also never appear in the accretion plots. The text says \"ρ+p>0 gives mass increase,\" which is only true if λB0+B1 > 0. For the same fitted dark-energy parameters, choosing B1 negative enough reverses the inequality, and the identical equations would predict mass decrease. Figures 3–5 therefore do not demonstrate the headline result. This is load-bearing, not cosmetic.\n\nThere is also a minor-to-moderate internal inconsistency: Table I lists CBDRM λ = 0.339 ± 0.037 with prior [0, 0.1], and ω1 = 1.756 ± 0.017 with prior [0, 0.1]; similarly CDMMA λ = −0.082 ± 0.004 with prior [0, 0.1]. Posterior means far outside the prior range suggest a mistake in prior definitions or in the sampling setup. And λ is treated as an independent free parameter even though Eq. (2) defines λ = δ/R; the paper never reconciles these.\n\nThe specialization to two EOS parameterizations is genuinely new, and the paper is honest about its lineage. But as it stands, the conclusion is not supported by the equations, so I would not accept it without major revision. For a referee: this is worth a careful read because the fix is straightforward — specify B1 (or an appropriate boundary condition) and redo the plots — and the explicit mass formulas would then be serviceable. I would send it to review with a request for major revision rather than desk-reject, since the core derivation is coherent and the gap is identifiable.","headline":"The paper derives new accretion mass formulas for two dark energy equations of state in generalized Rastall gravity, but the headline mass-increase claim does not follow because the sign of the accretion rate is controlled by an unconstrained integration constant.","tokens_in":22392,"tokens_out":3005,"would_cite":false,"duration_ms":24237,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.70.-s","95.36.+x","98.80.-k"],"model":"deepseek-v4-flash","headline":"This paper claims that in generalized Rastall gravity, a non-singular black hole accretes dark energy from both the CBDRM and CDMMA parameterizations in a way that increases its mass with cosmic time, and that the growth is consistent…","keywords":["dark energy parameterization","generalized Rastall gravity","black hole mass accretion","non-singular black hole","cosmological parameter constraints","CBDRM parameterization","CDMMA parameterization","mass-redshift relation"],"falsifier":"Take the paper's fitted parameter values, set B_1 so that lambda B_0 + B_1 is negative, and evaluate Eq. (35); if the predicted black-hole mass then decreases with time, the claimed growth is not a consequence of the constrained parameters alone. Alternatively, recompute Eq. (33) with lambda = delta/R from Eq. (2) rather than a constant and check whether the sign of dM/dt stays positive.","tokens_in":21204,"feed_emoji":"🕳️","tokens_out":9659,"duration_ms":86902,"temperature":0.7,"pith_summary":"This paper tries to establish that a non-singular black hole in generalized Rastall gravity gains mass as the Universe expands, provided the dark energy follows either of two recently proposed dynamical equation-of-state parameterizations (CBDRM and CDMMA) with parameters fitted to cosmological data. The authors derive the mass-accretion equation for the black hole, insert the Markov chain Monte Carlo constrained parameter values, and plot mass against redshift; both models show monotonic growth from early times to the present, whereas phantom-like fluids with negative pressure would shrink the hole. If the claim is right, dark energy accretion is a concrete mechanism that couples black hole growth to cosmic acceleration, and the generalized Rastall framework, with its varying Rastall parameter acting like a running cosmological constant, can reproduce and extend the standard Lambda-CDM behavior. The paper also uses the fitted parameters to compare the two models with Lambda-CDM and reports that CDMMA provides the best AIC-based balance of fit and complexity.","feed_headline":"Black holes gain mass as dark energy drives expansion","feed_subtitle":"A generalized Rastall gravity analysis with data-fitted parameters predicts steady growth, matching the accelerating-universe picture.","key_machinery":"The load-bearing object is the modified energy-momentum conservation law $T^{{mu nu}}$;_{; mu} = ($\\lambda$ R)^{, nu} with $\\lambda$ = delta/R, which turns the generalized Rastall field equations into Einstein equations with a varying cosmological-constant-like term. From this, the paper derives the accretion rate equation $\\dot{M} = 4\\pi(\\lambda B_0 + B_1)(\\rho+p)M^2$, whose sign is fixed by the combination of the Rastall parameter $\\lambda$, the geometric factor $B_0 = (4f(r)/r - 2r f''(r))$, and the integration constant B_1. The mass equation (35) is then obtained by integrating this rate using the generalized conservation equation, with the Hubble parameter and energy densities for each dark-energy parameterization inserted. The non-singular black hole metric $f(r) = 1 - C_1/r - \\epsilon\\delta r^2/3 + \\epsilon a b^3/(3r) \\exp(-r^3/b^3)$ supplies the geometric factor B_0 and the horizon structure.","core_discovery":"The central claim is that Eq. (35), the redshift-space mass equation obtained from the generalized Rastall accretion formalism, yields an increasing black-hole mass for both the CBDRM and CDMMA dark-energy parameterizations once the parameters are fixed at their constrained values. For both models, the integrand contains the factor ((lambda B_0 + B_1)(1 - 3 epsilon lambda (1+omega(z))))/(1 - 4 epsilon lambda) times d rho / H(z), and with the constrained dark-energy equation of state giving positive rho+p, the integral over redshift is positive, so M(z) rises from early times to the present. The comparison plots show the same monotonic increase for the standard Lambda-CDM model, and the authors interpret the growth as the signature of dark energy's accelerating influence within generalized Rastall gravity.","pith_inferences":["An implication the paper leaves implicit is that the sign of the mass change is controlled by the freely adjustable combination lambda B_0 + B_1; until B_1 is fixed by data, the same formalism can produce either growth or shrinkage for identical dark-energy models.","A testable extension would be to predict the redshift-dependent mass growth as a correction to the local black-hole mass function; future gravitational-wave or quasar observations could search for the cumulative effect.","The paper treats lambda as a constant even though Eq. (2) defines it as delta/R; a fully self-consistent extension would couple the accretion rate back to the local Ricci scalar and allow the Rastall parameter to vary through the black hole's environment.","The same mass-equation machinery could be applied to other non-singular black hole solutions or other dark-energy parameterizations, since the main empirical content is not the sign alone but the predicted growth rate as a function of redshift."],"forward_implications":["Under both dark-energy parameterizations, a non-singular black hole in generalized Rastall gravity gains mass as the Universe expands, so dark-energy accretion acts as a growth mechanism rather than an evaporation mechanism.","Because the fitted dark-energy models have positive rho+p, the mass growth is tied to the accelerated expansion; the same accretion equation would predict mass loss for phantom-like fluids with rho+p<0.","The constrained parameter values place both models in the region where the mass integral in Eq. (35) is positive, so the qualitative mass-increase result holds within the reported 1 sigma and 2 sigma credible intervals.","The comparison with Lambda-CDM shows the same qualitative growth but different rates, implying that dark-energy accretion does not distinguish the models by sign alone but could distinguish them by rate.","If the result is correct, the growth mechanism could leave an imprint on the late-time mass function of black holes, connecting the accretion process to cosmic acceleration in a directly observable way."],"supporting_citations":[{"why":"It supplies the generalized Rastall gravity framework, including the non-conservation law and the varying Rastall parameter definition.","marker":"[42]"},{"why":"It provides the modified Friedmann equations and the generalized conservation equation used to build the cosmological background.","marker":"[44]"},{"why":"It develops the explicit conservation equation and Hubble-parameter forms for generalized Rastall gravity.","marker":"[45]"},{"why":"It supplies the non-singular black hole metric and the mass-accretion setup on which the paper's accretion equations rest.","marker":"[47]"},{"why":"It introduces the CBDRM equation-of-state parameterization and its energy-density expression.","marker":"[19]"},{"why":"It introduces the CDMMA parameterization and its energy-density expression.","marker":"[20]"},{"why":"It establishes the baseline result that negative-pressure fluids shrink black holes, the behavior this paper contrasts with dark-energy accretion.","marker":"[23]"},{"why":"It supplies the type Ia supernova compilation used as one of the observational datasets in the parameter constraints.","marker":"[67]"},{"why":"It supplies one of the baryon acoustic oscillation datasets used in the constraints.","marker":"[69]"}],"fun_headline_variants":["Rastall gravity: dark energy makes black holes grow","Black holes accrete dark energy, gain mass","Constrained parameters show black hole mass rise","Dark energy accretion boosts black hole mass","Data-fitted Rastall model predicts black hole growth"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion rests on the unconstrained integration constant B_1 making lambda B_0 + B_1 positive, yet the paper assigns B_1 no value or prior, so the same equations would predict mass loss for a sufficiently negative B_1.","fun_headline_variants_meta":{"raw":{"variants":["Rastall gravity: dark energy makes black holes grow","Black holes accrete dark energy, gain mass","Constrained parameters show black hole mass rise","Dark energy accretion boosts black hole mass","Data-fitted Rastall model predicts black hole growth"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000316,"raw_usage":{"total_tokens":1832,"prompt_tokens":1027,"completion_tokens":805,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":643,"completion_tokens_details":{"reasoning_tokens":731}},"tokens_in":643,"tokens_out":805,"duration_ms":6027,"temperature":1.0,"reasoning_tokens":731,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:06:38.223758+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the paper's fitted parameter values, set B_1 so that lambda B_0 + B_1 is negative, and evaluate Eq. (35); if the predicted black-hole mass then decreases with time, the claimed growth is not a consequence of the constrained parameters alone. Alternatively, recompute Eq. (33) with lambda = delta/R from Eq. (2) rather than a constant and check whether the sign of dM/dt stays positive.","supporting_citations":[{"cited_title":"Testing the Rastall's theory using matter power spectrum","cited_arxiv_id":"1004.4603","evidence_quote":"It supplies the generalized Rastall gravity framework, including the non-conservation law and the varying Rastall parameter definition."},{"cited_title":"Lin, W.-L","cited_arxiv_id":null,"evidence_quote":"It provides the modified Friedmann equations and the generalized conservation equation used to build the cosmological background."},{"cited_title":"Ziaie, H","cited_arxiv_id":null,"evidence_quote":"It develops the explicit conservation equation and Hubble-parameter forms for generalized Rastall gravity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the non-singular black hole metric and the mass-accretion setup on which the paper's accretion equations rest."},{"cited_title":"Estimation of $H_0$ and $r_d$ in the $\\omega(z)$ Parameterization within Einstein and Horava-Lifshitz Gravity Using DESI-Y1 and SDSS-IV","cited_arxiv_id":"2405.15874","evidence_quote":"It introduces the CBDRM equation-of-state parameterization and its energy-density expression."},{"cited_title":"Khurana, H","cited_arxiv_id":null,"evidence_quote":"It introduces the CDMMA parameterization and its energy-density expression."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It establishes the baseline result that negative-pressure fluids shrink black holes, the behavior this paper contrasts with dark-energy accretion."},{"cited_title":"Escobal, J","cited_arxiv_id":null,"evidence_quote":"It supplies one of the baryon acoustic oscillation datasets used in the constraints."}],"review_version":1}