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REVIEW 3 major objections 4 minor 44 references

Constraints on unimodular diffusion models with latest observables

T0 review · 3 major / 4 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2607.09750 v1 pith:ZPOIUDAA submitted 2026-07-04 physics.gen-ph

Jesús Chavarría , Sebastien Fromenteau , Daniel Sudarsky , Mariana Vargas-Magaña This is my paper · ORCID
classification physics.gen-ph
keywords unimodulargravitydiffusiondynamicaldarkenergyDESIDR2DESY5H0tensionenergy-momentumnon-conservation
topics The Hubble TensionDark Energy
open problems Dark MatterThe Hubble Tension
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

The unimodular continuity equation ρ̇_m + 3H ho_m = −ρ̇_Λ, closed by a three-parameter phenomenological profile for ho_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.

What would settle it

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 ho_Λ of the preferred magnitude.

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Extended reading notes

Core claim

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 ho_Λ and not significantly alleviating the H0 tension.

Load-bearing premise

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [§3.3, Table 4] 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 imes 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.
  2. [§4, Tables 2–3] 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.
  3. [§2.1–2.2, §4] 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.
minor comments (4)
  1. [§2.1, Fig. 1] 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.
  2. [§2.2, Table 1] §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.
  3. [Appendix B] 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.
  4. [Throughout] 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.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: phenomenological step/arctan forms for ρ_Λ are chosen a priori, then constrained by external data in ordinary MCMC inference; self-citations supply only the UG motivation.

  1. self citation load bearing [§1 (Introduction) and §2.1 (Discrete model)]
    "In [2], such a violation of energy conservation was studied as a diffusion mechanism affecting matter (dark and baryonic), leading to an effective dark energy component within the framework of unimodular gravity. ... The discrete model parametrization (see figure 1) considers a proposed expression for ρ_Λ of the form [eq. 2.2]"

    The discrete model and the broader UG-diffusion interpretation are taken from prior work by overlapping authors. This is only motivational scaffolding; the present paper’s new continuous model, the MCMC constraints, and the ΔDIC values are computed afresh against external data and do not reduce to the citation.

full rationale

The derivation chain is: UG continuity equation (1.3) + phenomenological ansatz for ρ_Λ(a) (discrete step eq. 2.2 or continuous arctan eq. 2.5) → analytic ρ_b, ρ_c via proportional partition (eqs. 2.3–2.4, 2.15–2.16, 2.18–2.19) → CLASS implementation → MCMC fit of free parameters (a*, δ, Δρ_Λ plus standard cosmology) to independent Planck 2018 + DESI DR2 + DESY5 likelihoods → report posteriors and ΔDIC/AIC/BIC vs ΛCDM. Nothing is forced by construction: the functional forms are not derived from the data, the sign of Δρ_Λ is left free (and often prefers the “wrong” sign), and the information criteria are computed from the actual posterior samples. Self-citations ([2], [15–19]) justify the theoretical setup and the original discrete model but do not enter the likelihood or uniqueness claims; the observational results stand independently. Minor self-citation for motivation is normal and non-load-bearing, yielding score 1 rather than 0. Weaknesses (energy budget vs local BH density, negative mean Δρ_Λ) are assumption/correctness issues, not circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The observational claim rests on standard FLRW + unimodular trace-free Einstein equations with a non-conserved T_μν, plus three free diffusion parameters and a proportional baryon/CDM partition. The physical story (BH granularity, CSL, particle friction) motivates the sign and epoch of J but is not used to fix the functional form or amplitude; those are fitted. Invented/postulated entities are the diffusion current channels and the effective time-dependent Λ as their integral.

free parameters (5)
  • Δρ_Λ (diffusion amplitude) = continuous flat mean −0.0159±0.0349; discrete ~0.0001±0.084
    Strength of energy transfer between matter and effective dark energy; fitted with flat prior U(−0.2,0.2) or U(0,0.2).
  • a* (transition midpoint scale factor) = continuous flat mean 0.393±0.279; discrete 0.223±0.192
    Controls when the diffusion becomes important; fitted U(0.02,1).
  • δ (transition width) = continuous flat mean 0.527±0.301; discrete 0.435±0.274
    Duration of the step/arctan transition; different prior domains for discrete vs continuous.
  • Ω_k (spatial curvature, extended run) = mean 0.0028±0.0013
    Optional free curvature in continuous model.
  • α = Ω_b/(Ω_b+Ω_c) partition of diffusion = set by Ω_b, Ω_c
    Assumes baryons and CDM contribute to J in proportion to present abundances; fixed by that ratio rather than independently measured.
assumptions (5)
  • domain assumption Unimodular gravity field equations with effective Λ(x)=Λ0+∫J, reducing to Friedmann and continuity equations (1.2)–(1.3).
    Core theoretical framework taken from prior UG literature; not re-derived here.
  • domain assumption Homogeneous isotropic FLRW cosmology with only non-relativistic matter participating in diffusion.
    Stated in §2; radiation and neutrinos not diffused.
  • ad hoc to paper ρ_Λ(a) takes the discrete step form (2.2) or continuous arctan form (2.5).
    Phenomenological choices approximating an unknown J(t) from BH/CSL physics; not derived from f_BH(M,J).
  • ad hoc to paper Baryon and CDM densities each receive a share of the integrated diffusion proportional to present Ω_b and Ω_c (eqs. 2.18–2.19).
    Partition is motivated but not unique; required for CMB implementation.
  • standard math Standard statistical model comparison via AIC, BIC, DIC and Burnham–Anderson scale.
    Used in §3.3; authors themselves note BIC/DIC limitations for CMB-like data.
invented entities (2)
  • Diffusion current J from BH–granularity friction (and optional CSL/particle channels)
    purpose: Physical source of energy non-conservation that builds effective dynamical Λ.
    Postulated via modified geodesic/spin equations (1.4)–(1.5); no independent cosmological measurement of J is provided; energy-budget tension noted in §4.
  • Effective time-dependent cosmological constant as cumulative ∫J
    purpose: Replace or augment a fixed Λ and vacuum-energy contribution.
    Emerges from UG once ∇·T≠0; dynamical form is fitted rather than predicted from microphysics.

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Pith. "Pith review of Constraints on unimodular diffusion models with latest observables." pith.science (2026). https://pith.science/paper/ZPOIUDAA

@misc{pith2026260709750,
  author       = {Pith},
  title        = {Pith review of: Constraints on unimodular diffusion models with latest observables},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZPOIUDAA}},
  note         = {Machine review of arXiv:2607.09750}
}
abstract

Cosmological models incorporating a time-dependent equation of state have recently been explored \cite{DESI:2025fii}, showing a preference for a dynamical dark energy component. In this work, we investigate a scenario in which an effective, time-dependent cosmological constant arises as an emergent manifestation of a violation of energy-momentum conservation. In \cite{Landau:2022mhm}, such a violation of energy conservation was studied as a diffusion mechanism affecting matter (dark and baryonic), leading to an effective dark energy component within the framework of unimodular gravity. Here, we present an updated analysis using the more recent Type Ia supernova data set from the Dark Energy Survey (DESY5) and the baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), along with the CMB temperature, polarization, and lensing data from Planck 2018. Our results identify a transition phase that occurs at intermediate times, with slight evidence in favor of the model relative to the $\Lambda$CDM according to the $\mathrm{\Delta DIC}$ criterion. Interestingly, a non-decisive preference for an evolution corresponding to either a time-decreasing or time-increasing effective cosmological constant is found. However, slightly higher values of $H_0$ favor a time-increasing effective cosmological constant. Although the $H_0$ tension is not significantly alleviated, these results suggest that a more refined modeling of the physics of the diffusion mechanism may offer a viable route toward addressing the current discrepancy in the Hubble expansion rate, while also providing a natural framework for incorporating a dynamical dark energy and addressing the problem of vacuum energy contribution.

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