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REVIEW 4 major objections 4 minor 68 references

A dissipative version of unimodular gravity — with a diffusion term tied to bulk viscosity — fits late-time cosmological data as well as ΛCDM, while making the cosmological constant an integration constant.

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2026-08-03 08:20 UTC pith:ALHAUVDB

load-bearing objection A competent, honestly-reported fit of a known expansion-history family, but the claimed diffusion–viscosity link is a reparameterization, not a tested constraint, and the data do not require dissipation. the 4 major comments →

arxiv 2601.17281 v2 pith:ALHAUVDB submitted 2026-01-24 gr-qc

Dissipative Unimodular Gravity: Linking Energy Diffusion to Bulk Viscosity as an Alternative to ΛCDM under DESI DR2 Data

Norman Cruz , Esteban Gonz\'alez , Guillermo Palma This is my paper
classification gr-qc
keywords unimodular gravitybulk viscosityenergy diffusioncosmological constant problemlate-time cosmologydark energybaryon acoustic oscillationsHubble tension
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that the loss of energy-momentum conservation inherent to unimodular gravity can feed a bulk viscosity of the cosmic fluid, and that the resulting expansion history is observationally competitive with the standard dark-energy model. With the ansätze Q = νH² and ξ = ξ0|Q|^{1/2} it obtains an analytic Hubble parameter and fits it to supernovae, baryon acoustic oscillations, cosmic chronometers, gravitational lensing, and black-hole shadow data. The best-fit diffusion parameter ν is small but systematically nonzero across datasets, and the best-fit Hubble constant shifts toward the higher values preferred by local distance-ladder measurements. A sympathetic reader should care because, if true, the cosmological constant ceases to be an unexplained coupling, and a very small violation of energy conservation becomes compatible with observations.

Core claim

The central claim is that in the trace-free formulation of unimodular gravity, where the cosmological constant arises as an integration constant, adding a first-order relativistic bulk viscosity whose coefficient scales as ξ = ξ0|Q|^{1/2} with the energy-diffusion function Q yields a closed analytical solution for H(z). With the diffusion function set to Q = νH², the effective vacuum energy acquires a running term, ρ_vac = Λ + νH², and fits to late-time data favor ν slightly different from zero. Both the dissipative model and its non-dissipative limit (ξ0 = 0) achieve lower χ²_min than ΛCDM for every dataset combination, stay competitive under the Bayesian Information Criterion, and move H0

What carries the argument

The load-bearing ingredients are the diffusion function Q = νH² — the integrated nonconservation of the energy-momentum tensor that arises from the restricted diffeomorphism invariance — and the bulk viscosity ξ = ξ0|Q|^{1/2} = ξ0|ν|^{1/2}|H|, introduced through a first-order relativistic fluid theory. Plugging these into the unimodular Friedmann equations produces the first-order differential equation (28) for H, whose exact solution (29) is the model confronted with data. The conceptual move is to interpret Λ + Q as a time-dependent effective cosmological constant, so the vacuum energy is running by construction.

Load-bearing premise

Everything hinges on the particular functional forms Q = νH² and ξ = ξ0|Q|^{1/2}, chosen for solvability rather than derived from the theory; if the true diffusion or viscosity has a different dependence on density or expansion rate, the analytical solution and the fitted conclusions change.

What would settle it

Take the best-fit non-dissipative value ν ≈ 0.16 and compute the predicted growth of matter density fluctuations at z ≈ 1; current and near-future galaxy surveys measure growth to roughly 1–2 percent precision, so if growth matches standard ΛCDM rather than the diffusion-suppressed prediction, the claimed energy diffusion is excluded.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Two variants of the model (dissipative and non-dissipative) reach lower χ²_min than ΛCDM on every dataset combination, while the fixed-coupling case ξ0 = 1 is strongly disfavored by the Bayesian Information Criterion.
  • In the non-dissipative limit the fitted diffusion parameter sits at ν ≈ 0.16 ± 0.05, clearly excluding zero; in the dissipative model ν is consistent with zero within its larger errors, so the preference for a nonzero diffusion effect is carried mainly by the simpler model.
  • The best-fit H0 rises from about 70.0 for ΛCDM to roughly 72.3–73.4 km/s/Mpc, moving toward the higher value obtained from local distance-ladder measurements.
  • Because the cosmological constant is an integration constant, the vacuum-energy density can in principle be reset by absorbing quantum-field contributions, which is the paper's proposed path around the cosmological constant problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The proportionality ξ ∝ |Q|^{1/2} is a chosen linking rule rather than a derived relation; if a future microphysical model provides an independent expression for Q(ρ, H), the fitted ν can be checked directly against predicted diffusion rates, offering a clean falsification test.
  • A nonzero ν effectively mimics a dark-energy equation of state that varies with time, so the model offers a physical reinterpretation of recent baryon acoustic oscillation results that hint at evolving dark energy — without introducing a scalar field.
  • Because the diffusion term removes energy from the matter sector, the framework predicts small changes in the growth of cosmic structure; comparing the model's growth predictions with galaxy-clustering data could distinguish it from ΛCDM.
  • The first-order fluid treatment used here is known from other contexts to have short-timescale instability issues; a causal extension (with a relaxation time for the viscous pressure) would preserve the analytic expansion history but change its time-dependent behavior at early times.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper constructs a late-time FLRW cosmological model in unimodular gravity in which the matter fluid experiences Eckart bulk viscosity and an energy-diffusion function Q. The authors choose the ansatze Q = νH² and ξ = ξ0|Q|^{1/2} = ξν0|H|, derive an analytic H²(z) solution, and fit it to Pantheon+ SNe, cosmic chronometers, DESI DR2 BAO, H0LiCOW lensing, and EHT black-hole-shadow data. They compare the dissipative UG model, its non-dissipative limit, the constrained case ξ0 = 1, and ΛCDM using χ²_min and BIC, and conclude that the dissipative and non-dissipative UG models are competitive with ΛCDM and that a small but nontrivial diffusion parameter ν is favored by observations.

Significance. If the central claims were supported, the paper would provide a useful demonstration that a unimodular-gravity extension with diffusion and dissipation can describe late-time expansion as well as ΛCDM while avoiding the cosmological-constant fine-tuning. The algebraic derivation from the chosen ansatze to Eq. (29) is internally consistent, the MCMC setup is standard, and the use of five independent data sets is a strength. However, the paper's headline novelty—the diffusion–viscosity link ξ = ξ0|Q|^{1/2}—is not actually tested because ξ0 is free, and the only constrained version (ξ0 = 1) is strongly disfavored. In the free-ξ0 dissipative model, ν is consistent with zero in every dataset combination, so the claim that the data favor a nontrivial energy nonconservation is not supported by that model. These issues affect the abstract and conclusions and require a substantial reframing rather than cosmetic changes.

major comments (4)
  1. [§III, Eq. (27); Table II] The claimed link between diffusion and bulk viscosity is not tested by the general dissipative UG fit. Equation (27) merely defines ξν0 ≡ ξ0|ν|^{1/2}; since ξ0 is a free positive parameter, any pair (ν, ξν0) with ν ≠ 0 can be represented by choosing ξ0 = ξν0/|ν|^{1/2}. The only version in which Eq. (27) is a genuine constraint is ξ0 = 1, which forces ξν0 = |ν|^{1/2}, and that model is strongly disfavored by the data (ΔBIC = −18.6, −20.5, −13.8 in Table II). Thus the abstract's claim that the paper links energy diffusion to bulk viscosity is unsupported by the statistical analysis; the general model is effectively a two-parameter extension of ΛCDM with independent diffusion and viscosity parameters.
  2. [Table I; §V and §VI] The conclusion that the diffusion parameter ν is 'non-negligible across all datasets' is contradicted by the dissipative UG rows of Table I: ν = (0.36 ± 9.75)×10⁻², (0.84 ± 9.32)×10⁻², and (−1.08 ± 9.58)×10⁻² for the three dataset combinations. Each is consistent with zero at well below 1σ. The only case with ν significantly positive is the UG model without dissipation, where ν = (19.60 ± 4.80)×10⁻², etc., but that model has no viscosity and therefore no diffusion–viscosity link. The paper should state this distinction and revise the abstract and Section VI accordingly.
  3. [§III, Eq. (29); §VI] Equation (29) is acknowledged to have been previously obtained in Ref. [42] for a running-vacuum model with dissipative dark matter in GR, under the identifications noted in the text. The present paper's UG interpretation changes the theoretical narrative, but the fitting function and parameter space are mathematically the same. Consequently, the statistical comparison with ΛCDM does not discriminate between the UG origin and the earlier GR running-vacuum origin. The novelty of the paper therefore rests entirely on the interpretive claim embodied in Eq. (27), which, as noted above, is not constrained by the data. The authors should either provide a genuinely discriminating prediction or explicitly state that the data cannot distinguish their construction from Ref. [42].
  4. [Abstract; Table II] The phrase 'significantly better fit to the data (χ²min)' overstates the evidence. The χ²_min improvements for the dissipative UG model are sizable for SNe+BAO (Δχ² = 19.5), but the BIC differences are small and dataset-dependent: ΔBIC = +4.6 for SNe+BAO, −3.0 for SNe+BAO+CC, and +0.6 for the joint analysis. By the paper's own BIC criterion, these are not significant or are even negative. 'Significantly better fit' should be restricted to χ²_min, and the BIC results should be reported as inconclusive or mildly in favor of ΛCDM for the SNe+BAO+CC combination.
minor comments (4)
  1. [Table I, ξ0 = 1 rows] For the constrained model ξ0 = 1, the relation ξν0 = |ν|^{1/2} implies that the reported central values are mutually inconsistent on their face: e.g., for SNe+BAO, ν = 0.06×10⁻² gives |ν|^{1/2} ≈ 0.024, while the reported ξν0 = 0.040. Since the text says ξν0 was estimated directly from the MCMC chains, the discrepancy may arise from reporting posterior means of a nonlinear function, but this should be stated explicitly and the table footnoted.
  2. [General] There are several typographical issues: 'bayronic' for baryonic, 'whithout' for without, 'dissipative UG gravity' in Section V, and the notation Δχ²_min in Section V appears with squared parentheses that are likely unintended. These should be corrected.
  3. [§IV F, Eq. (59)] The inequality in Eq. (59) is imposed to avoid a complex Hubble parameter, but its effect on the posterior is not discussed. In particular, the prior range ξν0 ∈ (0, √3) combined with ν ∈ (−3, 3) may exclude large parts of parameter space; a sentence explaining the resulting effective prior would improve transparency.
  4. [§III, ansatz discussion] The motivation for Q = νH² is tied to running-vacuum models, but the paper does not explain why the diffusion function in UG should take this specific form rather than, e.g., Q ∝ ρ as in Ref. [16]. Since the entire statistical analysis depends on this choice, a brief discussion of its robustness—or lack thereof—would be useful.

Circularity Check

2 steps flagged

The claimed diffusion–viscosity link is definitional: Eq. (27) merely redefines the fitted parameter ξν0, and the only constrained version (ξ0=1) is strongly disfavored; the 'non-negligible' ν is a fitted input, not a prediction.

specific steps
  1. self definitional [Section III, Eqs. (26)–(27) and the paragraph following them]
    "we propose the following ansätze for the diffusion function and the bulk viscosity: Q = νH², ξ = ξ0|Q|^{1/2} = ξν0 |H|, where ν is an arbitrary dimensionless parameter and ξν0 ≡ ξ0|ν|^{1/2} is also a dimensionless parameter, with ξ0 > 0 ... It is important to note that the bulk viscosity and the diffusion function are linked through the parameter ν"

    Substituting (26) into (27) gives ξ = ξ0|ν|^{1/2}|H| ≡ ξν0|H|. In the MCMC, ξν0 is a free parameter (θ = {h, Ωb,0, ΩDM,0, ν, ξν0}). For any ν ≠ 0 and any fitted ξν0 > 0 there exists ξ0 = ξν0/√|ν| > 0, so Eq. (27) imposes no constraint on the model; it is a reparameterization. The general dissipative UG model is therefore parametrically the same as the running-vacuum GR model with independent diffusion and viscosity parameters—the paper admits Eq. (29) was 'previously found in [42]'. The only version where the link is a real constraint, ξ0 = 1, is strongly disfavored (ΔBIC = −13.8 to −20.5 in Table II). Claiming that the data support the link is thus true by construction of the ansatz, not by evidence.

  2. fitted input called prediction [Section V, Results and Discussions; Section VI, Conclusions]
    "Regarding the best-fit value for ν, note that across all considered datasets, it remains close to zero but is non-negligible. ... One of the most significant findings of our analysis is that the diffusion parameter ν is non-negligible across all datasets"

    ν is one of the free parameters fitted to the same data through Eq. (29); its posterior mean is the fit output, not an independent prediction. In Table I, every dissipative UG fit gives ν consistent with zero at ≲0.1σ—e.g., joint ν = (−1.08 ± 9.58)×10⁻²—and only the no-dissipation limit (ξ0 = 0) has a significantly positive ν, in which case there is no diffusion–viscosity link to test. Presenting the fitted, statistically insignificant ν as 'one of the most significant findings' converts the fitted input into the claimed result.

full rationale

The MCMC fit itself is not circular: the theoretical H²(z) with fitted parameters is compared against SNe Ia, BAO, CC, GL, and BHS data, with BIC penalties applied, so the claim that the model is competitive with ΛCDM has independent empirical content. No load-bearing self-citation chain or imported uniqueness theorem was found: [42] is properly cited for the previous form of the solution, and [16,43] are used as motivation rather than as proof. The circularity lies in the advertised 'link' between diffusion and viscosity. Equation (27) is a definitional reparameterization because ξν0 is fitted as a free parameter; the one nontrivial version of the link, ξ0 = 1, is strongly disfavored by the data. The additional claim that ν is non-negligible is a restatement of the fitted posterior, and in the dissipative model that posterior is actually consistent with zero. Thus the central novelty—linking energy diffusion to bulk viscosity—reduces by construction to the fitted ansatz, while the empirical model comparison remains legitimate. Score 6 reflects this partial circularity rather than complete equivalence.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The model rests on two ad hoc functional forms (Q = νH² and ξ = ξ0|Q|^{1/2}) plus the standard UG diffusion equation and Eckart theory. There are no new fundamental entities; the fitted parameters ν, ξν0, h, Ωb, ΩDM, M carry the full empirical content.

free parameters (6)
  • h (reduced Hubble constant H0 = 100h km/s/Mpc) = 0.723 ± 0.007 (dissipative UG, joint)
    Fitted in MCMC; drives all distance scales; H0 is central to the claimed SH0ES agreement.
  • Ωb,0 (baryon density parameter) = 0.042 ± 0.001 (joint)
    Fitted with Gaussian prior on Ωb,0 h² from BBN; enters sound horizon and expansion.
  • ΩDM,0 (cold dark matter density parameter) = 0.309 ± 0.015 (joint)
    Fitted; required by Eq. (29) and the flatness constraint.
  • ν (diffusion coefficient in Q = νH²) = -0.011 ± 0.096 (dissipative joint); 0.161 ± 0.041 (non-dissipative joint)
    Fitted free parameter; the claim of energy nonconservation is the posterior value of this fitted parameter.
  • ξν0 (bulk viscosity coefficient in ξ = ξν0 H) = 0.029 ± 0.015 (dissipative joint)
    Fitted free parameter; consistent with zero, so dissipation is not required by data.
  • M (SNe Ia absolute magnitude nuisance) = -19.28 ± 0.02 (dissipative joint)
    Fitted nuisance parameter needed for Pantheon+ distance moduli.
axioms (6)
  • domain assumption UG field equations imply ∇μ(Tμν − gμν Q) = 0 with Q an arbitrary path integral (Eq. 14)
    Taken from Refs. [16,34]; foundational to the model; no independent derivation in this paper.
  • domain assumption Eckart's first-order bulk viscosity, ΔTμν = −3Hξ(gμν + uμuν) (Eq. 16)
    Standard but known to be acausal/unstable; the compatibility with non-conservation in UG is asserted, not proven.
  • ad hoc to paper Ansatz Q = νH² (Eq. 26)
    Chosen for analytic solvability and motivated by running-vacuum models, not derived from UG.
  • ad hoc to paper Ansatz ξ = ξ0|Q|^{1/2} = ξν0 |H| (Eq. 27)
    The claimed link between dissipation and diffusion is assumed, not derived; effectively a ξ∝H parametrization.
  • ad hoc to paper All matter (baryons+DM) is a single pressureless fluid (γ = 1) experiencing the same diffusion and viscosity, with Λ > 0
    Assumed in Section III; physically baryons should not have bulk viscosity; this assumption affects the fit.
  • domain assumption Parameter constraint Eq. (59) to keep H² positive
    A consistency condition on fitted parameters; it restricts the priors and could bias posterior if not accounted as an informative constraint.

pith-pipeline@v1.3.0-alltime-deepseek · 19975 in / 21973 out tokens · 233871 ms · 2026-08-03T08:20:10.973748+00:00 · methodology

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read the original abstract

In this paper, we perform a theoretical and observational study of the presence of viscosity in the Unimodular Gravity formalism, a pioneering approach that, to the best of our knowledge, has not been previously considered within the present context. Specifically, we study a flat FLRW universe at late times, where matter experiences dissipative processes in the form of a bulk viscosity, in the framework of Eckart's theory, which is linked to the energy diffusion function $Q$ through the power law $\xi=\xi_{0}\left|Q\right|^{1/2}$, being $\xi_{0}$ a positive dimensionless parameter. By assuming the Ansatz $Q=\nu H^{2}$, where $H$ is the Hubble parameter and $\nu$ is a dimensionless arbitrary constant, we find analytical solutions for the cosmological evolution. We test these models against the most recent cosmological observations, including type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, gravitational lensing, and black hole shadow data. Our results show that two of the tested models provide a significantly better fit to the data ($\chi_{\text{min}}^{2}$) and remain as competitive as the $\Lambda$CDM model according to the Bayesian Information Criterion. These findings, combined with the inherent ability of Unimodular Gravity to alleviate the cosmological constant problem, position dissipative UG as a robust and compelling alternative to the standard model, potentially suggesting that a very small but nontrivial energy nonconservation is compatible with the late-time observational data.

Figures

Figures reproduced from arXiv: 2601.17281 by Esteban Gonz\'alez, Guillermo Palma, Norman Cruz.

Figure 1
Figure 1. Figure 1: FIG. 1. The posterior 1D distributions and joint marginalized [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The posterior 1D distributions and joint marginalized [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The posterior 1D distributions and joint marginalized [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

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