{"id":"c460fa68-2fe2-406f-8dbe-bbf8d6c30e0c","arxiv_id":"2607.09750","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Unimodular diffusion models with latest DESI/DESY5/Planck data show intermediate-time transitions and only mild, non-decisive preference over ΛCDM without resolving H0.","lead":"Updated cosmological fits of unimodular-gravity diffusion models with DESY5, DESI DR2, and Planck 2018 find only slight DIC preference over ΛCDM and no clear sign for energy flow. The H0 tension is not meaningfully eased, though the framework still offers a route to dynamical dark energy without vacuum-energy gravitating.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"The load-bearing soft spot is that the three-parameter ρ_Λ forms and proportional matter partition are treated as adequate proxies for the cumulative J of the physical mechanisms, yet the data prefer the opposite sign and an energy budget that exceeds local BH density.","rationale":"The Reader correctly isolates the weakest link: the three-parameter phenomenological ρ_Λ(a) plus proportional matter partition is asked to stand in for the cumulative J of the microphysical mechanisms that motivate the whole framework. The data’s preference for negative Δρ_Λ and the energy-budget mismatch with local BH density make that proxy insecure, exactly as the Reader notes. No stronger internal inconsistency appears—the CLASS implementation, the CMB imprint via early Ω_b,c (eqs. 2.20–2.23), and the information-criterion discussion are competent—so the verdict remains CONDITIONAL rather than REJECT. The concrete test above would settle whether the reported intermediate-time transition and mild ΔDIC preference survive once the phenomenological forms are replaced by (or at least constrained by) a more realistic J(t). Until that check is done, the paper is a useful observational update but should not be read as decisive evidence for UG diffusion.","tokens_in":20626,"tokens_out":797,"duration_ms":7520,"concrete_test":"Re-run the continuous-model MCMC (Planck 2018 + lensing + DESI DR2 + DESY5) with a physically motivated J(t) constructed from a simple PBH or Pop-III BH mass function that evolves under the spin-diffusion term of eq. 1.5 (or, at minimum, replace the single arctan by a two-component sum of a positive BH term and a negative CSL term as in eq. 3.1). If the resulting posterior still yields ΔDIC ≲ −1.5 relative to ΛCDM and a transition at intermediate a, the phenomenological claim is robust; if the preference disappears or the sign of the net Δρ_Λ is forced positive only at the cost of worse fit, the load-bearing assumption fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim (slight ΔDIC preference for a transition at intermediate times, non-decisive on the sign of Δρ_Λ) rests on the assumption that the discrete step (eq. 2.2) or continuous arctan (eq. 2.5), together with the proportional split of the diffusion term into baryons and CDM (eqs. 2.3–2.4, 2.15–2.16, 2.18–2.19), adequately represent the cumulative current J arising from BH–granularity friction, CSL, or particle diffusion (§1, eqs. 1.4–1.5, 3.1). That assumption is least secure: unconstrained posteriors give mean Δρ_Λ < 0 (Table 2: −0.0159 ± 0.0349 continuous flat; Table 3: −0.0339 ± 0.0473 with curvature), opposite to the energy-transfer direction required by the BH-spin story, while the positive-prior run still yields an implied energy density ~1.69×10^9 M_⊙/Mpc^{3} that exceeds the observed local BH mass density by orders of magnitude (§4). The paper itself flags both issues and notes that a realistic f_BH(M,J) is unavailable, so the phenomenological forms remain unanchored. Consequently the reported “slight evidence” and the suggestion that refined modeling could address H0 are only as strong as this proxy; if the forms do not capture the true J(t), the intermediate-time transition and the ΔDIC values become artifacts of the chosen parametrization rather than support for the UG diffusion mechanism.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper updates constraints on unimodular-gravity diffusion models in which a time-dependent effective cosmological constant arises from non-conservation of the energy-momentum tensor (current J). Two phenomenological forms for ρ_Λ(a) are implemented in CLASS—a discrete step (Eq. 2.2) and a continuous arctan (Eq. 2.5)—with the diffused energy partitioned between baryons and CDM proportionally to present-day abundances (Eqs. 2.18–2.19). Using Planck 2018 TT/TE/EE+lensing, DESI DR2 BAO and DESY5 supernovae, the authors report an intermediate-time transition (a* ~ 0.2–0.4), non-decisive preference for the sign of Δρ_Λ, a mild ΔDIC preference over flat ΛCDM (especially when curvature is free), and only a modest upward shift in H0 that does not resolve the Hubble tension. They interpret the results as encouraging for refined modeling of black-hole–granularity or CSL diffusion within unimodular gravity.","tokens_in":21194,"tokens_out":1374,"duration_ms":19116,"significance":"If the intermediate-time transition and mild DIC preference survive more rigorous model comparison and a better-motivated J(t), the work would supply a concrete, observationally constrained realization of dynamical dark energy that simultaneously addresses the vacuum-energy problem of unimodular gravity. The implementation in CLASS, the public-data MCMC pipeline, the individual-probe consistency checks (Appendix A), and the explicit energy-budget comparison with local black-hole density are strengths that make the constraints reusable. Even a null or negative result on the sign of Δρ_Λ would still be useful for ruling out simple BH-spin diffusion scenarios.","major_comments":[{"comment":"Table 4 and §3.3: BIC strongly disfavors both UG models (ΔBIC ~ +25–30), DIC mildly favors them (especially with curvature), and the text then elevates AIC as “most balanced” after noting that DIC’s Gaussian-unimodal assumptions are only partially satisfied. This selective ranking is load-bearing for the abstract’s claim of “slight evidence \times relative to ΛCDM according to the ΔDIC criterion.” A more robust comparison (nested Bayesian evidence, or at least a clear statement that no criterion yields decisive preference) is required before the mild DIC numbers can be advertised as evidence.","section":"§3.3, Table 4"},{"comment":"Tables 2–3 and §4: unconstrained posteriors prefer Δρ_Λ < 0 (continuous flat: −0.0159 ± 0.0349; with curvature: −0.0339 ± 0.0473), opposite to the energy-transfer direction required by the black-hole spin-diffusion mechanism that motivates the model (Eqs. 1.4–1.5, 3.1). The positive-prior run still implies an energy density ~1.69 × 10^9 M_⊙ Mpc^−3, orders of magnitude above the observed local BH mass density. The paper flags both issues yet continues to present refined BH modeling as a “viable route” for H0. Either the physical interpretation must be restricted to mechanisms that allow negative J (e.g., CSL), or the conclusions must be rewritten to reflect that the data do not support the original BH-diffusion picture.","section":"§4, Tables 2–3"},{"comment":"Eqs. 2.2, 2.5, 2.18–2.19 and the discussion in §1 and §4: the three-parameter step/arctan forms plus the proportional partition α = Ω_b/(Ω_b+Ω_c) are treated as adequate proxies for the cumulative current J arising from BH–granularity friction, CSL or particle diffusion. The paper itself notes that a realistic f_BH(M,J) is unavailable and that the energy budget is problematic. Because the reported intermediate-time transition and the ΔDIC values rest on these proxies, their adequacy needs either a quantitative justification (e.g., matching to a toy BH population) or an explicit caveat that the results are purely phenomenological and do not yet test the underlying microphysics.","section":"§2.1–2.2, §4"}],"minor_comments":[{"comment":"Figure 1 caption and §2.1: the discrete-model parameters are labeled Δρ, a*, δ, ρ_Λ0, yet later text and Table 1 use Δρ_Λ ≡ (8πG/3)Δρ/100^{2}. A single consistent definition should be stated at first appearance.","section":"§2.1, Fig. 1"},{"comment":"§2.2: the continuous model switches the prior domain of δ to [0.002,1] because “no unique mapping exists.” A short quantitative statement of the approximate correspondence (e.g., δ_cont ≈ δ_disc/10 for abrupt transitions) would help readers compare the two posteriors in Fig. 5.","section":"§2.2, Table 1"},{"comment":"Appendix B: the claim that conventional ω0–ωa parametrizations “fail to capture” the UG models is left qualitative. A brief plot or table of the effective w(a) reconstructed from the best-fit continuous/discrete solutions would make the comparison concrete.","section":"Appendix B"},{"comment":"Typographical: “Continous” appears repeatedly (Figs. 3–5, Table 2, etc.); “unimodular” is occasionally capitalized inconsistently; Eq. (2.7) line-breaking makes the arctan argument hard to parse.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid data-update of the authors’ earlier UG-diffusion papers and is appropriate for JCAP. The main risk is over-interpretation of a criterion-dependent mild preference and of a phenomenological proxy that the data themselves disfavor. Once the three major points are addressed (or the claims are correspondingly softened), the paper should be publishable. No concerns about citation pattern or novelty disclosure."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a competent update of the Landau et al. (2023) unimodular-diffusion program to DESY5 + DESI DR2 + Planck 2018. What is new is the continuous arctan parametrization of ρ_Λ(a), the curvature extension, the individual-probe consistency checks, and the fresh posteriors. The CLASS+Cobaya pipeline is standard and cleanly reported; tables and contours are usable.\n\nThe paper does the analysis carefully. It flags that unconstrained runs prefer mean Δρ_Λ < 0 (opposite the BH-spin energy-transfer direction), that the positive-prior energy budget exceeds local BH mass density by orders of magnitude, and that a realistic f_BH(M,J) is unavailable. It also notes that BIC strongly disfavors the models while DIC mildly favors them, then elevates AIC as the most balanced criterion. That is honest bookkeeping rather than over-claim.\n\nThe soft spot is real but already acknowledged: the three-parameter step/arctan forms plus proportional matter partition are phenomenological proxies for the cumulative current J. If those forms do not capture the true J(t), the intermediate-time transition and the Δ DIC values are artifacts of the parametrization. The H0 shift remains tiny. None of this is hidden; the abstract and discussion state the non-decisive sign preference and the limited H0 relief.\n\nWho it is for: people already working on unimodular gravity, energy non-conservation, or dynamical-DE phenomenology who want the latest numerical constraints. It is not a decisive case for the mechanism. A serious editor should send it to referees; the methods and data are solid enough to deserve that time, even if the physical interpretation stays provisional. I would cite the new posteriors if I were writing on related models, and I would bring the paper to a reading group that already cares about UG or DESI dynamical-DE results.","headline":"Solid observational update of unimodular diffusion models on DESY5+DESI DR2+Planck; mild DIC preference for an intermediate transition, but the preferred sign of Δρ_Λ often conflicts with the BH-motivation story and H0 is barely moved.","tokens_in":21751,"tokens_out":523,"would_cite":true,"duration_ms":4908,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Unimodular diffusion of matter into an effective cosmological constant shows a mid-history transition and slight preference over flat ΛCDM on latest DESI, DESY5 and Planck data.","keywords":["unimodular gravity","diffusion","dynamical dark energy","DESI DR2","DESY5","H0 tension","energy-momentum non-conservation"],"falsifier":"A joint analysis that freezes the diffusion parameters to zero and recovers a statistically worse DIC, or an independent measurement of the black-hole mass-spin density that cannot supply the energy budget implied by a positive Δ\rho_Λ of the preferred magnitude.","tokens_in":21554,"feed_emoji":"⭐","tokens_out":724,"duration_ms":6468,"temperature":0.7,"pith_summary":"The paper tests whether an effective, time-dependent cosmological constant can arise simply from a mild violation of energy-momentum conservation in unimodular gravity, rather than from a new dark-energy fluid. Matter (baryons and cold dark matter) is allowed to diffuse into this effective Λ according to a three-parameter step or arctan profile; the resulting densities are evolved in CLASS and constrained with Planck 2018 CMB, DESI DR2 BAO and DESY5 supernovae. The data prefer a transition at intermediate redshifts and give a modest improvement over ΛCDM on the deviance information criterion, especially once spatial curvature is free. The sign of the diffusion is not decisive, yet slightly higher H0 values accompany a positive (matter-to-dark-energy) flow. The authors present the framework as a natural way to obtain dynamical dark energy while automatically screening vacuum-energy contributions, and they note that a more refined microphysical model of the diffusion current could further ease the Hubble tension.","feed_headline":"Unimodular diffusion finds mid-history dark-energy transition","feed_subtitle":"Latest DESI, DESY5 and Planck data give slight preference over ΛCDM; H0 barely moves","key_machinery":"The unimodular continuity equation ρ̇_m + 3H\rho_m = −ρ̇_Λ, closed by a three-parameter phenomenological profile for \rho_Λ(a) (step or arctan) that encodes the cumulative non-conservation current J, with the transferred energy partitioned between baryons and cold dark matter in proportion to their present abundances.","core_discovery":"With Planck 2018 + DESI DR2 + DESY5, both discrete and continuous unimodular diffusion models identify a transition phase at intermediate cosmic times and yield slight evidence relative to ΛCDM according to ΔDIC (especially when curvature is allowed), while remaining non-decisive on the sign of Δ\rho_Λ and not significantly alleviating the H0 tension.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Unimodular diffusion spots mid-era dark-energy transition","DESI-DESY5-Planck data slightly prefer unimodular DE models","Intermediate-time DE shift found in unimodular diffusion","Slight ΔDIC nod to unimodular models over ΛCDM","Non-decisive sign for evolving cosmological constant in diffusion"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"That a simple three-parameter step or arctan form for the effective cosmological-constant density, with matter split only by present-day abundance ratios, adequately captures the cumulative diffusion current from black-hole spin, spontaneous collapse or granular friction.","fun_headline_variants_meta":{"raw":{"variants":["Unimodular diffusion spots mid-era dark-energy transition","DESI-DESY5-Planck data slightly prefer unimodular DE models","Intermediate-time DE shift found in unimodular diffusion","Slight ΔDIC nod to unimodular models over ΛCDM","Non-decisive sign for evolving cosmological constant in diffusion"]},"model":"grok-4.5","effort":"low","cost_usd":0.005616,"raw_usage":{"total_tokens":1576,"prompt_tokens":864,"num_sources_used":0,"completion_tokens":74,"cost_in_usd_ticks":56160000,"prompt_tokens_details":{"text_tokens":864,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":638,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":864,"tokens_out":74,"duration_ms":7580,"temperature":1.0,"reasoning_tokens":638,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T16:29:19.724485+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A joint analysis that freezes the diffusion parameters to zero and recovers a statistically worse DIC, or an independent measurement of the black-hole mass-spin density that cannot supply the energy budget implied by a positive Δ\rho_Λ of the preferred magnitude.","supporting_citations":[],"review_version":1}