Looking for interactions in the cosmological dark sector

Cassio Pigozzo; Humberto A. Borges; Jailson S. Alcaniz; Micol Benetti; Saulo Carneiro; Welber Miranda

REVIEW 3 major objections 5 minor 7 cited by

Looking for interactions in the cosmological dark sector

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Using CMB, supernova, and local-Hubble data, this paper finds the dark-sector interaction parameter α is consistent with zero at 1σ, with its preferred sign flipping when Neff is freed.

desk verdict A competent, incremental constraint on a specific interacting vacuum model: alpha stays consistent with zero, and the negative shift under Neff is a 1-sigma wiggle, not evidence. read the letter →

arxiv 1908.07213 v1 pith:CEWL4N4W submitted 2019-08-20 astro-ph.CO

Micol Benetti , Welber Miranda , Humberto A. Borges , Cassio Pigozzo , Saulo Carneiro , Jailson S. Alcaniz This is my paper · ORCID

classification astro-ph.CO

keywords darkenergymatterinteractingsectorΛ(t)CDMgeneralizedChaplygingasHubbletensioncosmologicalperturbationsCMB

topics Dark Energy Dark Matter The Hubble Tension

open problems The 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

This paper tests whether dark matter and dark energy exchange energy beyond gravity by fitting a one-parameter interacting model, $Λ(t)$CDM, to CMB, supernova, local-Hubble, and deuterium data. The central result is that the interaction parameter $α$ is compatible with zero at $1σ$ in every variant tested. The minimal model leans positive (energy flowing from matter to dark energy), while admitting extra relativistic degrees of freedom shifts the preference to negative $α$ (dark energy converting into dark matter). The model also lowers the Hubble-constant tension from about 3.4σ to about 2.25σ, but mostly by broadening the allowed ranges rather than moving the central value to the local measurement. If the paper is right, no non-gravitational interaction is currently required by this data combination, though the door is left open for one.

What carries the argument

The load-bearing object is the ansatz $Λ = σH^{-2α}$, which turns the Friedmann and conservation equations into a generalized Chaplygin-gas background, $E(z)=[(1-Ω_{m0})+Ω_{m0}(1+z)^{3(1+α)}]^{1/(1+α)}+Ω_{R0}(1+z)^4$. The perturbation sector is built on the decomposition $T_{μν}=ρ_m u_μu_ν + Λg_{μν}$ and the assumption that the vacuum perturbation vanishes in the comoving frame, $δΛ_c=0$, so matter follows geodesics and the Poisson equation retains its standard form. This machinery converts a single parameter $α$ into predictions for the CMB spectra, the matter power-spectrum turnover $k_{eq}$, and the growth rate $fσ_8$, and it is what lets the parameter scan map $α$ against $H_0$, $A_l$, and $N_{eff}$.

What would settle it

Measure the matter power-spectrum turnover $k_{eq}$ and the growth rate $fσ_8$ at percent-level precision. Equation (2.18) predicts $k_{eq}=0.073$ Mpc$^{-1} h^2 Ω_{m0}^{1/(1+α)}$, so an independent $k_{eq}$ and $Ω_{m0}$ give $α$ without CMB; if that value disagrees with the CMB-derived $α$, the perturbation treatment is at fault. More simply, a future CMB experiment that fixes $N_{eff}=3.046$ and returns $|α|<0.01$ at 95% would falsify the paper's positive hint, while a local $H_0$ above 72 km/s/Mpc combined with $N_{eff}$ fixed to 3.046 would falsify the interaction-based relaxation of the Hubble tension.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that current CMB + JLA + $H_0$ + deuterium data do not require any non-gravitational dark-sector interaction when the interaction is parametrized by $Λ = σH^{-2α}$. The posterior for $α$ is centered at $0.037±0.050$ for the minimal $Λ(t)$CDM model and at $-0.018±0.047$ when both the lensing amplitude $A_l$ and $N_{eff}$ are freed; both are within $1σ$ of zero. With $A_l$ free the $H_0$ tension drops from ≃3.41σ to ≃2.25σ, and with $N_{eff}$ free the model simultaneously allows lower $σ_8$ and higher $H_0$, easing both tensions at the price of doubled errors. The paper thus claims the data are consistent with no interaction, with the preferred sign of the energy flux depending on whether extra relativistic degrees of freedom are admitted.

Load-bearing premise

The perturbation analysis assumes the vacuum component stays perfectly smooth in the comoving frame ($δΛ_c=0$) with no momentum transfer ($δQ=0$), so only matter clusters; if $Λ$ clusters or exchanges momentum, the inferred $α$, $H_0$, $A_l$, and $N_{eff}$ would shift and the no-interaction conclusion could change.

Editorial extensions

If this is right

If $α=0$ is the true value, $Λ$CDM remains a sufficient description of this data combination, and the slight positive $α$ seen in the minimal fit is a statistical fluctuation.
A positive $α$ in the minimal model means matter is converted into dark energy, which shifts $H_0$ upward by less than 1 km/s/Mpc and does not by itself close the 3.4σ gap to the local distance ladder.
When $A_l$ and $N_{eff}$ are freed, the data favor negative $α$—an energy flux from dark energy to dark matter—together with $N_{eff}=3.22±0.14$, and this combination allows lower $σ_8$ at higher $H_0$.
The reported relaxation of the $H_0$ tension to 2.25-2.65σ comes from roughly doubling the uncertainty on $H_0$, not from a central value that reaches the local measurement.
In the $A_l+N_{eff}$ extension, values $H_0>70$ km/s/Mpc and $σ_8<0.82$ are allowed at 1σ, a combination the standard model does not easily produce.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The sign flip of $α$ between the minimal and $N_{eff}$-extended fits points to a strong degeneracy between the interaction and the relativistic-energy content; fixing $N_{eff}$ with future CMB or laboratory neutrino measurements would break it and decide the flux direction.
The relaxation of the tensions by error inflation suggests that the model is not so much predicting a higher $H_0$ as accommodating it; a forecast that holds the error budget fixed could separate the two.
Because the model's perturbation sector assumes $δΛ_c=0$, a detection of nonzero $α$ would be interpreted as matter creation from a smooth vacuum; a detection of clustered dark energy would require a different perturbation theory and would change the meaning of the same $α$.
The background-level equivalence with a generalized Chaplygin gas means distance-only data can constrain $α$ without the perturbation assumptions; comparing such constraints with the CMB-derived $α$ would isolate whether the perturbation model is driving the result.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Plainly: this paper does a workmanlike job of putting a particular Lambda(t)CDM model through a Planck 2015 + JLA + H0 + D/H pipeline, and it finds the interaction parameter alpha is consistent with zero at 1-sigma in all variants. That is the headline result, and I believe it. The negative alpha preferred in the Neff extension is a posterior mean shift at 1-sigma, not a detection; the abstract's 'favour' is too strong.

The genuinely new bit is the combined likelihood with Al and Neff left free. The model and perturbation equations come from the authors' own prior papers, but the combined posterior, including the sign shift and the H0/σ8 plane behavior, is a new number. I'd credit them for being explicit that everything is compatible with zero.

Soft spots, in order. First, the perturbation scheme assumes an exactly smooth vacuum (δΛ_c=0, δQ=0). That is a physical choice, not an identity, and the paper never tests whether a different clustering prescription changes the posterior. This is the main limitation and should be acknowledged in the text. Second, the equations (2.23)-(2.25) are cited from earlier work, not re-derived; that's fine for a subfield paper, but it means the referee can't check the implementation without the code. No code is released. Third, Figure 1 is a copy-paste artifact from a different paper — the captions don't match the surrounding text, and it needs to be replaced or removed. Fourth, the H0 tension relaxation claim is real but modest: they widen the error bars by adding parameters, and 2.25σ is still a discrepancy.

The self-citation pattern is fine here; they're building on their own program and citing it. No construction-level circularity.

Who is this for? People working on interacting dark energy or generalized Chaplygin gas models, who need a recent reference constraint on this specific ansatz. It's a solid but narrow contribution. I'd accept it for peer review with requests for code release, a sensitivity test on the vacuum perturbation assumption, and a clearer abstract. It doesn't deserve a central slot in the literature, but it deserves a fair referee.

Referee Report

3 major / 5 minor

Summary. This paper analyses a family of interacting dark-sector models, Λ(t)CDM, defined by the background ansatz Λ = σH^{-2α} (Eq. 2.11), where α=0 recovers ΛCDM. The authors couple Planck 2015 TT+lowP CMB data with JLA supernovae, an HST prior on H0 and a deuterium-abundance prior on Ωb0h2, and run CLASS/MontePython to constrain α together with the standard cosmological parameters, optionally freeing the lensing amplitude Al and Neff. The central quantitative results in Table 1 are that α is consistent with zero at 1σ in every model variant considered; the posterior mean is slightly positive for the minimal Λ(t)CDM model and slightly negative when Al and Neff are freed; and the inferred H0 is shifted upward, reducing the CMB-versus-local H0 discrepancy from roughly 3.4σ to about 2.25σ–2.65σ. The paper also discusses growth-of-structure and RSD signatures of the model.

Significance. The paper's main result—that current CMB and low-redshift data do not require α≠0, while the posterior mean moves with Neff/Al—is a useful, falsifiable check of a simple interacting-dark-sector parametrization. The comparison across four model variants is informative, and the numbers in Table 1 make the statistical statement explicit. The significance is moderated, however, by the fact that the CMB-level analysis relies on perturbative equations that are adopted from previous work under a smoothness assumption for Λ, and by the absence of code or validation material for the modified CLASS implementation.

major comments (3)

[Section 2.2, Eqs. (2.7)-(2.8), (2.23)-(2.28)] The perturbation system is derived under the assumption δΛ_c≈0 and δQ≈0, which is a physical prescription on how the vacuum component responds to inhomogeneities rather than a consequence of the background relation Λ=σH^{-2α}. If Λ is allowed to cluster or to exchange momentum with dark matter, the source terms in the dark-matter and Poisson equations change and the CMB spectra—and therefore the α posterior in Table 1—can shift. This sensitivity is not tested; the central claim that the data show no preference for interactions is therefore conditional on this prescription and should be flagged as such, or supplemented with a comparison to alternative perturbation schemes.
[Abstract and Table 1] In the Λ(t)CDM+Al+Neff case, Table 1 reports α = −0.018±0.047, which is fully compatible with zero at 1σ. The abstract's wording that the data 'favour negative values of α' overstates the result; the data only show a negative posterior mean. Please rephrase to avoid implying a detection.
[Section 4] The numerical implementation of Eqs. (2.23)-(2.28) in CLASS is not validated in the paper and no chains or code are released. Because the constraints are produced by this implementation, the authors should provide at least a consistency test—for example, recovering ΛCDM for α=0 and matching a published spectrum for the exactly solvable α=−1/2 case—so that the central numbers can be independently checked.

minor comments (5)

[Figure 1] Figure 1 appears to contain a block of text copied from another paper, including equation numbers (59)-(68), 'FIG. 4', and references [61] and [63], together with a new caption; this must be corrected.
[Eq. (2.14)] In Eq. (2.14), the notation 'z3' should read '(1+z)^3' to avoid ambiguity.
[Eq. (2.13)] In Eq. (2.13), the placement of the square root and the exponent 1/(1+α) should be checked; the present typesetting is easy to misread.
[Table 1] Table 1 reports χ2/2 values; please specify whether these are −2lnL/2 and how the JLA light-curve recalibration is included.
[Eq. (2.24)] Eq. (2.24) contains the ratio Q'/Q, which is singular in the α→0 limit; clarify how CLASS handles this limit, since α=0 is the ΛCDM reference point.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circularity: α is constrained by external data; only minor, non-load-bearing self-citations appear.

full rationale

The paper's central result is a Bayesian fit of the interaction parameter α to external likelihoods (TT+lowP, JLA, HST H0 prior, deuterium abundance). The model is defined by the explicit ansatz Λ = σH^{-2α} (Eq. 2.11), and the perturbation equations of Section 2.2 are derived under the explicitly stated assumption that there is no momentum transfer in the dark matter rest frame (δQ = 0) and that the vacuum perturbation δΛ_c vanishes (Eq. 2.8). These are physical modeling assumptions, not definitions of the target result: the constraint on α is not obtained from an equation equivalent to itself, and no fitted parameter is renamed as a prediction. The references to earlier work by the same group (e.g., [27], [45], [47]) supply the perturbation framework and the ansatz, but the ansatz is transparently written out in the text and the perturbation scheme is supported by external textbook references such as [46]; these citations do not forbid alternatives or force the posterior. The claimed reduction of the H0 tension is a comparison between the fitted posterior (which includes the H0 prior) and that same prior, but this is a standard internal-consistency diagnostic rather than a construction-level equivalence. Overall, the analysis is data-driven and externally falsifiable, so there is no significant circularity; the score reflects only the presence of minor self-citations in the perturbation setup, which are not load-bearing.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The standard LambdaCDM parameters (omega_b, omega_cdm, tau, As, ns) and foreground nuisance parameters are also fitted, but they are not model-specific and are not counted here. The model-specific degrees of freedom are alpha, Al, and Neff. No new particle or force is introduced; the interaction is a phenomenological energy-momentum transfer parameterized by alpha. The smoothness of the vacuum perturbation and the adiabatic initial conditions are the main untested premises.

free parameters (3)

alpha (interaction parameter) = 0.037 +/- 0.050 (minimal); 0.059 +/- 0.066 (+Al); -0.018 +/- 0.047 (+Al+Neff)
Central parameter controlling dark sector energy transfer; it is fitted to data, not predicted, and defines the model under test.
Al (lensing amplitude) = 1.18 +/- 0.07 (+Al); 1.14 +/- 0.07 (+Al+Neff)
Extra free parameter in the extensions; its high preferred value affects the posterior of alpha and the H0 comparison.
Neff (effective relativistic degrees of freedom) = 3.22 +/- 0.14
Free in the last extension; the abstract's claim of negative alpha is obtained only when Neff is freed, so this fitted parameter drives the second headline result.

assumptions (5)

domain assumption FLRW spacetime with a perfect fluid decomposed as T_mu_nu = rho_m u_mu u_nu + Lambda g_mu_nu.
Eq. (2.2) splits the cosmic fluid into clustering pressureless matter and a vacuum component; all background equations follow from this decomposition.
ad hoc to paper Interaction ansatz Lambda = sigma H^{-2 alpha}, with sigma = 3(1 - Omega_m0) H0^{2(alpha+1)}.
Eq. (2.11) defines the Lambda(t)CDM model under test; it is a phenomenological parameterization not derived from a fundamental theory and it restricts the class of interactions considered.
domain assumption The vacuum component is exactly smooth in the comoving frame, delta Lambda_c = 0, and there is no momentum transfer, so delta Q = 0.
This is used after Eqs. (2.7)-(2.8) to write the perturbed dark matter and Poisson equations (2.23)-(2.28); it is load-bearing for the CMB spectra computation.
domain assumption Baryons and radiation conserve as in LambdaCDM, with interaction only in the dark sector.
Section 2.2 keeps the standard perturbation equations for baryons and radiation; if baryons also interacted, the constraints would change.
domain assumption Purely adiabatic scalar initial conditions, flat priors, sum of neutrino masses fixed to 0.06 eV, and Neff = 3.04 in the minimal model.
Section 4 states these analysis choices; non-adiabatic modes, nonzero curvature priors, or different neutrino mass assumptions are not explored.

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Pith. "Pith review of Looking for interactions in the cosmological dark sector." pith.science (2026). https://pith.science/paper/CEWL4N4W

@misc{pith2026190807213,
  author       = {Pith},
  title        = {Pith review of: Looking for interactions in the cosmological dark sector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CEWL4N4W}},
  note         = {Machine review of arXiv:1908.07213}
}

abstract

We study observational signatures of non-gravitational interactions between the dark components of the cosmic fluid, which can be either due to creation of dark particles from the expanding vacuum or an effect of the clustering of a dynamical dark energy. In particular, we analyse a class of interacting models ($\Lambda$(t)CDM), characterised by the parameter $\alpha$, that behaves at background level like cold matter at early times and tends to a cosmological constant in the asymptotic future. In our analysis we consider both background and primordial perturbations evolutions of the model. We use Cosmic Microwave Background (CMB) data together with late time observations, such as the Joint Light-curve Analysis (JLA) supernovae data, the Hubble Space Telescope (HST) measurement of the local value of the Hubble-Lema\^itre parameter, and primordial deuterium abundance from Ly$\alpha$ systems to test the observational viability of the model and some of its extensions. We found that there is no preference for values of $\alpha$ different from zero (characterising interaction), even if there are some indications for positive values when the minimal $\Lambda$(t)CDM model is analysed. When extra degrees of freedom in the relativistic component of the cosmic fluid are considered, the data favour negative values of $\alpha$, which means an energy flux from dark energy to dark matter.

Figures

Figures reproduced from arXiv: 1908.07213 by the authors.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples,

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BAHAMAS: New Analysis of Type Ia Supernovae Reveals Inconsistencies with Standard Cosmology,

H. Shariﬀ, X. Jiao, R. Trotta and D. A. van Dyk, “BAHAMAS: New Analysis of Type Ia Supernovae Reveals Inconsistencies with Standard Cosmology,” Astrophys. J. 827, no. 1, 1 (2016)

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Alleviating the H0 and σ8 anomalies with a decaying dark matter model,

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Interacting scenarios with dynamical dark energy: observational constraints and alleviation of the H0 tension,

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Interacting dark energy after the latest Planck, DES, and H0 measurements: an excellent solution to the H0 and cosmic shear tensions,

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Velocities as a probe of dark sector interactions,

K. Koyama, R. Maartens and Y. S. Song, “Velocities as a probe of dark sector interactions,” JCAP 0910, 017 (2009)

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Inhomogeneous vacuum energy,

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Non-adiabatic perturbations in decaying vacuum cosmology,

W. Zimdahl, H. A. Borges, S. Carneiro, J. C. Fabris and W. S. Hipolito-Ricaldi, “Non-adiabatic perturbations in decaying vacuum cosmology,” JCAP 1104, 028 (2011)

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Cosmological perturbations,

K. A. Malik and D. Wands, “Cosmological perturbations,” Phys. Rept. 475, 1 (2009)

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A cosmological concordance model with dynamical vacuum term,

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An Alternative to quintessence,

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High - redshift objects and the generalized Chaplygin gas,

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Generalized Chaplygin gas, accelerated expansion and dark energy matter uniﬁcation,

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Uniﬁcation of dark matter and dark energy: The Inhomogeneous Chaplygin gas,

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Constraints on Chaplygin quartessence from the CLASS gravitational lens statistics and supernova data,

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Non-adiabatic Chaplygin gas,

H. A. Borges, S. Carneiro, J. C. Fabris and W. Zimdahl, “Non-adiabatic Chaplygin gas,” Phys. Lett. B 727, 37 (2013)

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Observational tests of non-adiabatic Chaplygin gas,

S. Carneiro and C. Pigozzo, “Observational tests of non-adiabatic Chaplygin gas,” JCAP 1410, 060 (2014)

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Cosmological constraints on a decomposed Chaplygin gas,

Y. Wang, D. Wands, L. Xu, J. De-Santiago and A. Hojjati, “Cosmological constraints on a decomposed Chaplygin gas,” Phys. Rev. D 87, no. 8, 083503 (2013)

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The Revival of the uniﬁed dark energy - dark matter model?,

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Nonvacuum initial states for cosmological perturbations of quantum mechanical origin,

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Number Counts and Dynamical Vacuum Cosmologies,

N. C. Devi, H. A. Borges, S. Carneiro and J. S. Alcaniz, “Number Counts and Dynamical Vacuum Cosmologies,” Mon. Not. Roy. Astron. Soc. 448, no. 1, 37 (2015)

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Modern Cosmology,

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Growth of structure in interacting vacuum cosmologies,

H. A. Borges and D. Wands, “Growth of structure in interacting vacuum cosmologies,” arXiv:1709.08933 [astro-ph.CO]

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Large-scale structure and integrated Sachs–Wolfe eﬀect in decaying vacuum cosmology,

H. Velten, H. A. Borges, S. Carneiro, R. Fazolo and S. Gomes, “Large-scale structure and integrated Sachs–Wolfe eﬀect in decaying vacuum cosmology,” Mon. Not. Roy. Astron. Soc. 452, no. 2, 2220 (2015)

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Planck 2015 results. XV. Gravitational lensing,

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Dynamical system analysis of interacting models,

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Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters,

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The Complete Light-curve Sample of Spectroscopically Conﬁrmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample,

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One Percent Determination of the Primordial Deuterium Abundance,

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The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes,

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Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code,

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Bayesian evidence against the Harrison-Zel’dovich spectrum in tensions with cosmological data sets,

E. Di Valentino, A. Melchiorri, Y. Fantaye and A. Heavens, “Bayesian evidence against the Harrison-Zel’dovich spectrum in tensions with cosmological data sets,” Phys. Rev. D 98, no. 6, 063508 (2018)

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On the concordance of cosmological data in the case of the generalized Chaplygin gas,

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Evidence for cosmological particle creation?,

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Interaction in the dark sector: a Bayesian analysis with latest observations,

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A search for sterile neutrinos with the latest cosmological observations,

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2017

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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Planck 2018 results. VI. Cosmological parameters,

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arXiv 2018

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Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM,

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Tensions between the Early and the Late Universe,

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KiDS+VIKING-450: Cosmic shear tomography with optical+infrared data,

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Cosmic Discordance: Are Planck CMB and CFHTLenS weak lensing measurements out of tune?,

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Is the H0 tension suggesting a fourth neutrino generation?,

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Hot Axions and the H0 tension,

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Early Dark Energy Can Resolve The Hubble Tension,

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