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Can decaying vacuum solve the H_0 Tension?

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that letting vacuum energy decay into dark matter can raise the high-redshift Hubble constant to about 71.6 km/s/Mpc, easing the Hubble tension and making a noninteracting universe inconsistent with the combined data at…

desk verdict A clean, honest test of two vacuum-decay models whose headline 5.8–6.2σ exclusion rests on LambdaCDM distance priors that may not transfer; worth refereeing, but the central claim needs full CMB validation. read the letter →

arxiv 2412.06756 v4 pith:3ZHHNUBB submitted 2024-12-09 astro-ph.CO gr-qc

L. S. Brito , J. F. Jesus , A. A. Escobal , S. H. Pereira This is my paper · ORCID
classification astro-ph.COgr-qc
keywords HubbletensiondecayingvacuumLambda(t)CDMdarkenergy-darkmatterinteractionPlanckdistancepriorscosmicchronometerstransversalBAOPantheon+supernovae
topics Dark MatterThe Hubble Tension
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

This paper asks whether letting the vacuum energy density decay into dark matter over cosmic time can relieve the Hubble tension, the persistent disagreement between local and early-universe measurements of the expansion rate. The authors study two simple interaction models and fit them to cosmic chronometer data, low-redshift supernovae with a local Hubble prior, transversal baryon acoustic oscillations, and Planck distance priors. For both models the combined fit returns a positive decay parameter and a Hubble constant around 71.6 km/s/Mpc, between the Planck value near 67.4 and the local distance-ladder value near 73.2, and it excludes the noninteracting case at at least 5.8 sigma. The residual disagreement shifts to the matter density, where low- and high-redshift data differ by roughly 2.1 sigma. If the result survives a full CMB analysis, vacuum decay becomes a concrete route toward resolving the tension.

What carries the argument

The central objects are the two interaction terms Q = 3epsilon H rho_Lambda (Model I) and Q = 3epsilon a H rho_Lambda (Model II), where Q is the energy transfer between dark matter and the vacuum. For Model I the vacuum density follows rho_Lambda proportional to $a^{{-3epsilon}}$, a generalized power-law decay in the scale factor; for Model II it decays exponentially, rho_Lambda = rho_Lambda* $e^{{-3epsilon a}}$. These closed forms turn the Friedmann equations into explicit H(z) expressions that are fit with epsilon as a free parameter. The single parameter epsilon does the load-bearing work: positive values raise the high-redshift H0 and are strongly preferred by the joint dataset.

What would settle it

Fit either model to the full Planck CMB likelihood instead of the compressed distance priors. If the decay parameter epsilon becomes consistent with zero at 95% confidence, or if the recovered H0 drops back toward 67-68 km/s/Mpc, the claimed noninteracting exclusion and the tension resolution are artifacts of the prior compression. A second check is to redo the joint fit with full three-dimensional BAO data, which the paper's comparison suggests would lower the significance.

Watch

Extended reading notes

Core claim

The central discovery claim is that both Lambda(t)CDM models, constrained by the combination of cosmic chronometers, low-redshift supernovae, transversal BAO, and Planck distance priors, require a positive interaction strength epsilon (0.0162+0.0029-0.0026 for the first model and 0.0209 ± 0.0036 for the second) and recover H0 = 71.63 ± 0.60 and 71.67 ± 0.60 km/s/Mpc. A positive epsilon means energy flows out of the vacuum into dark matter, and the high-redshift side's inferred H0 rises to meet the local distance ladder. The paper therefore claims that a noninteracting model is excluded at at least 5.8 sigma and that the Hubble tension is transformed into a milder roughly 2.1 sigma discrepancy in the matter density parameter, with the decay direction matching thermodynamic expectations.

Load-bearing premise

The whole high-redshift signal rests on Planck distance priors that were computed for the standard non-decaying model and then applied to the decaying models; the paper acknowledges this is approximate, and if those priors are biased for vacuum decay, the six-sigma exclusion of no decay is unsupported.

Editorial extensions

If this is right

  • If the central claim is right, a small vacuum-to-dark-matter decay at epsilon around 0.02 removes the 5-sigma-plus Hubble discrepancy in these models.
  • The residual roughly 2.1 sigma mismatch in the matter density becomes the next observational target, with low-redshift data preferring a higher matter density than high-redshift data.
  • The positive sign of epsilon matches thermodynamic arguments for the preferred decay direction and separates these models from fits that prefer the opposite transfer.
  • Model-comparison statistics in the paper favor both interacting models over flat LambdaCDM, so the data are not merely compatible with decay but prefer it.
  • Because epsilon correlates positively with H0, future local or early-universe measurements that sharpen H0 will directly tighten or challenge the required decay strength.

Reading between the lines

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

  • A testable corollary of the paper's own comparison is that dropping the local distance-ladder prior should substantially weaken the exclusion significance; the paper notes that an independent analysis without that prior found only 2.6-2.8 sigma evidence for interaction.
  • Replacing the compressed Planck distance priors with a full CMB likelihood fit is the obvious next check, and it would reveal whether the positive epsilon survives when the sound-horizon calibration is treated consistently inside the decaying-vacuum model.
  • If epsilon near 0.02 changes the matter-vacuum balance at late times, these models plausibly alter structure-growth predictions; a future test is whether the sigma8 tension shifts in the opposite direction from the H0 tension, as happens in some running-vacuum scenarios.
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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

2 major / 5 minor

Summary. The paper studies two phenomenological vacuum-decay models, Λ(t)CDM, with interaction terms Q=3ϵHρΛ (Model I) and Q=3ϵaHρΛ (Model II). The authors derive analytic H(z) expressions (Eqs. 16 and 27) and fit them to Cosmic Chronometers, Pantheon+&SH0ES, transversal BAO, and Planck distance priors using MCMC. They report H0≈71.63–71.67 km/s/Mpc, positive interaction strength ϵ≈0.016–0.021, and an exclusion of the noninteracting case ϵ=0 at 5.8–6.2σ. They interpret this as alleviating the H0 tension at the cost of a residual ~2σ tension in Ωm, and they compare the models to flat ΛCDM via AIC and BIC.

Significance. The analytic expressions for H(z) are a useful, clearly presented contribution, and the paper is refreshingly transparent about its main approximation: the CMB enters only through compressed Planck distance priors calibrated under flat ΛCDM, and the headline six-sigma exclusion depends on the validity of that transfer. If the distance-prior issue is resolved with a full Planck likelihood or an equivalent validation, the result would be significant: it provides a concrete interacting-dark-sector model that raises the high-redshift H0 and reduces the tension with SH0ES while making a falsifiable prediction of a mild Ωm tension. The authors' explicit caveats about the CMB approximation and the role of SH0ES are a strength. As it stands, however, the central claim is conditional rather than established.

major comments (2)
  1. [§III, Tables I and II; v4 abstract] The 'CMB' entry in the likelihood is the Planck 2018 distance priors of Chen, Huang, and Wang [40], which were calibrated under flat ΛCDM and validated in that paper only for flat ΛCDM, oΛCDM, and flat XCDM. The compressed quantities R, l_A, and ω_b are not sufficient statistics for the Λ(t)CDM models in Eqs. (16) and (27), because a nonzero ϵ changes both the background E(z) and the dark-matter perturbation evolution, so the mapping from model parameters to the CMB acoustic scale and peak shape differs. The text and the v4 abstract explicitly call this an 'approximated treatment,' and the conclusion defers a full CMB analysis to future work. This is the load-bearing premise for the 5.8–6.2σ exclusion of ϵ=0: if the distance priors are biased for Λ(t)CDM, the inferred ϵ and its significance could shift. I therefore treat the headline exclusion as conditional on validation of the distance-prior transfer with the full Planck likelihood.
  2. [Table IV] The model-comparison statistics are internally inconsistent. For the same datasets and the same number of free parameters, Model II is reported with a lower reduced χ²_ν (0.8853) than Model I (0.8910), yet Model II is assigned a higher AIC (ΔAIC=12.48) and higher BIC (ΔBIC=12.49). With χ²_ν≡χ²_min/(n−p) and AIC=χ²_min+2p (up to an irrelevant constant), a lower χ²_min for the same p implies a lower AIC and BIC, so the reported ordering is impossible. This inconsistency undermines the conclusion that 'both Model II and flat ΛCDM can be discarded' on the basis of ΔAIC>10 and ΔBIC>5, and it needs to be corrected.
minor comments (5)
  1. [Abstract (front matter)] The abstract preceding the main text reports H0=73.1±0.86 km/s/Mpc from 'Planck+SH0ES data,' whereas the main-text abstract and Tables I–III report H0≈71.63–71.67 km/s/Mpc for the combined CC+PS+BAO+CMB fit; the two versions should be harmonized.
  2. [§III] The quoted 2.1σ and 2.2σ tensions in Ωm between the low- and high-redshift constraints are not accompanied by a description of how the significance is computed; please state whether it is derived from the marginalized means and errors, from a joint posterior, or from a profile likelihood.
  3. [§II B] The polynomial Q(x) is used in Eq. (22) before it is defined in Eq. (24), and the same letter Q denotes the interaction term; renaming the polynomial (e.g., to S(x)) would avoid confusion.
  4. [§III C] The text calls the joint ΛCDM fit 'meaningless' because of the large discrepancies, yet Table III reports this combination; please clarify the status of that row.
  5. [§III D] The sentence attributing the difference with Ref. [48] mainly to the use of Pantheon+&SH0ES is too strong, since the CC+BAO+CMB-only fit in Tables I and II already excludes ϵ=0 at ≳5σ; the later mention of the different BAO choice is the more important difference and should lead.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: epsilon and H0 are free parameters estimated from data; no prediction reduces to an input by construction.

full rationale

The paper's central inference (epsilon > 0, H0 ~ 71.6 km/s/Mpc) comes from MCMC fits of free parameters epsilon, H0, Omega_m, and Omega_b to CC, Pantheon+&SH0ES, transversal BAO, and Planck distance priors through the model-specific Hubble functions in Eqs. (16) and (27). The decay parameter epsilon is not defined in terms of the output H0, and H0 is not a fitted quantity subsequently renamed as a prediction: the high-redshift combination CC+BAO+CMB alone gives epsilon = 0.0170+0.0031/-0.0027 and H0 = 71.93 +/- 0.79 km/s/Mpc for Model I (Table I), so the exclusion of epsilon = 0 is not forced by the inclusion of SH0ES in the combined fit. The Planck distance priors were compressed under flat LambdaCDM, and applying them to Lambda(t)CDM is an approximation that could bias the results; the authors explicitly acknowledge this in the abstract ('an approximated treatment to CMB') and in the text, but this is a model-transfer or correctness concern, not circularity, because the compressed values are not defined in terms of the fitted parameters. The self-citations (the transversal BAO sample of Ref. [41] and the thermodynamic preference argument of Ref. [32]) are data choices and supporting reasoning, not load-bearing derivations that reduce the central result to themselves. No equation or fitting step equates a predicted quantity with an input by construction.

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

The core model inputs are a flat FRW background, separate conservation for baryons and radiation, and the two phenomenological interaction terms. The analysis also assumes LambdaCDM-derived Planck distance priors transfer to these models. No free parameter is derived from first principles, but no new particles or fields are invented.

free parameters (5)
  • epsilon (interaction strength) = 0.0162 +0.0029 -0.0026 (Model I); 0.0209 +/- 0.0036 (Model II)
    The key parameter controlling the strength of vacuum decay; estimated from the data, not predicted. Its nonzero value is the paper's central evidence.
  • H0 = 71.63 +/- 0.60 (Model I); 71.67 +/- 0.60 (Model II) km/s/Mpc
    Current expansion rate, fitted jointly with the other parameters.
  • Omega_m = 0.2682 +/- 0.0062 (Model I); 0.2683 +/- 0.0061 (Model II)
    Total matter density parameter fitted to the data.
  • Omega_b = 0.04361 +/- 0.00075 (Model I); 0.04357 +/- 0.00075 (Model II)
    Baryon density parameter fitted to the data.
  • M (supernova absolute magnitude) = not reported in numerical tables
    Nuisance parameter shown in the corner plots but not quoted in the tables; needed for the Pantheon+SH0ES likelihood.
assumptions (5)
  • standard math Spatially flat Friedmann-Robertson-Walker metric with k=0 and standard Einstein equations.
    Used in Section II, Eqs. (1) and (2), as the background for all derivations.
  • domain assumption Baryons and radiation conserve separately, and only dark matter and vacuum exchange energy.
    Standard assumption isolating the interaction to the dark sector, stated in Eqs. (5) and (6).
  • ad hoc to paper The interaction terms Q=3 epsilon a^n H rho_Lambda with n=0 or 1 are the correct phenomenological forms of vacuum decay.
    Model I is from prior literature and Model II from Rajeev 1983; the paper does not derive these forms from a fundamental theory.
  • ad hoc to paper Planck 2018 distance priors from Chen et al. [40], calibrated under flat LambdaCDM, remain valid for Lambda(t)CDM models.
    Critical for the high-redshift constraints in Section III; the paper itself flags this as an approximation.
  • domain assumption The transverse BAO sample [41] is sufficiently model-independent for this analysis.
    The paper relies on this dataset's claim of weak model dependence when combining it with the distance priors.

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Pith. "Pith review of Can decaying vacuum solve the H_0 Tension?." pith.science (2026). https://pith.science/paper/3ZHHNUBB

@misc{pith2026241206756,
  author       = {Pith},
  title        = {Pith review of: Can decaying vacuum solve the H_0 Tension?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3ZHHNUBB}},
  note         = {Machine review of arXiv:2412.06756}
}
abstract

In the present work we analyze two different models of interaction between dark energy and dark matter, also known as vacuum decay models or $\Lambda(t)$CDM models. In both models, when the $H_0$ parameter is constrained by the Planck distance priors, its value is compatible with a higher value of $H_0$, in agreement with SH0ES data, while simultaneously reducing the values of $\Omega_m$ and $\Omega_b$. In both models, we find $H_0=73.1\pm0.86$ at 68\% c.l. by combining Planck+SH0ES data. We also find the decay parameter to be $\varepsilon=0.0197^{+0.0032}_{-0.0027}$ for one model and $\varepsilon=0.0203\pm0.0034$ for the other one. From these analyses, a noninteracting model is excluded at least at $6\sigma$ c.l.! This shows that these types of models are promising in solving or at least alleviating the $H_0$ tension problem. Our analysis also shows a preference for the decay of vacuum into dark matter, in agreement to thermodynamic analyses.

Figures

Figures reproduced from arXiv: 2412.06756 by the authors.

Figure 1
Figure 1. FIG. 1: Triangular plot of parameters, with data from Planck 2018 distance priors (CMB), Pan [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Triangular plot of parameters for the joint analysis of [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Triangular plot of parameters, with data from Planck 2018 distance priors (CMB), [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Triangular plot of parameters for the joint analysis of [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Triangular plot of parameters, with data from Planck 2018 distance priors (CMB), Pan [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

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Reviewed August 11, 2026 · model on record in the stance chip above.