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arxiv: 2606.20036 · v1 · pith:FCY3LACQnew · submitted 2026-06-18 · 🌌 astro-ph.CO · hep-ph· hep-th

Evolving Dark Energy Is Vacuum Energy After All

Dong Ha Lee , Carsten van de Bruck , Eleonora Di Valentino , Ludovic Van Waerbeke , Ariel Zhitnitsky This is my paper

Pith reviewed 2026-06-26 16:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-phhep-th
keywords QCD vacuumdynamical dark energyDESI observationsphantom crossingvacuum energycosmological fits
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The pith

A model of dark energy arising from the QCD vacuum fits observations and matches DESI hints without new fields or instabilities

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

The paper develops a cosmological implementation of dark energy emerging directly from the QCD vacuum's response to expanding spacetime. This approach reproduces the late-time evolution favored by DESI baryon acoustic oscillation data while fitting Planck, ACT, SPT-3G, and supernova samples. It achieves this without introducing new fundamental fields or degrees of freedom and avoids the instabilities typical of phantom scalar-field models. The fit remains stable across different choices for how the vacuum energy activates during expansion.

Core claim

The QCD-induced dark-energy model provides an excellent fit to the data and reproduces the late-time dark-energy evolution preferred by DESI observations while remaining free from theoretical instabilities.

What carries the argument

The global vacuum effect associated with the response of the non-perturbative topological structure of the QCD vacuum to an expanding spacetime, implemented via an activation mechanism.

Load-bearing premise

The QCD vacuum produces a specific time-dependent energy density in response to cosmic expansion through a chosen activation mechanism.

What would settle it

A future data set showing either no phantom-crossing behavior at intermediate redshifts or the emergence of theoretical instabilities in the effective equation of state would falsify the model.

Figures

Figures reproduced from arXiv: 2606.20036 by Ariel Zhitnitsky, Carsten van de Bruck, Dong Ha Lee, Eleonora Di Valentino, Ludovic Van Waerbeke.

Figure 1
Figure 1. Figure 1: β and a dβ d ln a for zq = ∆zq = 1. The dotted lines represent the outputs of the modified CLASS code for the same parameter values. 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 z 50 60 70 80 90 100 110 120 130 H(z) [k m / s / M p c] H (z) Hw0wa(z) Hexp Hexp(z) Htanh Htanh(z) (a) Form of H(z) for different cosmological models. The values of H are obtained by matching the cosmology to the required present￾d… view at source ↗
Figure 2
Figure 2. Figure 2: Background evolution functions for ΛCDM, w0waCDM, and the QCD-DE models for a given set of cosmological parameters. The chosen cosmological parameters are as follows: Ωm = 0.3, H0 = 67.75; w0 = −0.8, wa = −0.5 for w0waCDM; and zq = ∆zq = 1 for QCD-DE. The dotted lines represent the outputs of the modified CLASS code for the same set of parameters. past (wDE < −1). The phantom crossing in our model is consi… view at source ↗
Figure 3
Figure 3. Figure 3: The equation of state of DE, wDE ≡ PDE/ρDE, for ΛCDM, w0waCDM, and QCD-DE models. We modified the Cosmic Linear Anisotropy Solving System (CLASS) developed by D. Blas et al. 2011 to compute the QCD-DE cosmologies for β parametrized by Eqs. (22) and (23).5 The cosmology described by the model has eight parameters and uses the constraint 1 = PΩi to derive H given the choice of parameters and the value of ΩDE… view at source ↗
Figure 4
Figure 4. Figure 4: Triangle plot of cosmological parameter constraints for ΛCDM, w0waCDM, and the QCD-DE models obtained from the CMB-SPA+DD+DESI dataset combination. The corresponding constraints obtained with the CMB-SPA+PP+DESI dataset combination are fully consistent with those derived using DD for all models considered and are therefore not shown. specific functional form chosen for the switch mechanism, provided it sat… view at source ↗
Figure 5
Figure 5. Figure 5: Posterior reconstruction of the effective QCD-DE equation of state obtained from the CMB-SPA+DD+DESI dataset combination. The reference CPL curve is computed from the MAP w0waCDM cosmology fitted to the same dataset. For the same dataset combination, the corresponding constraints on the phantom crossing of the CPL parametrization is zphantom = 0.35+0.08 −0.07. With constraints from observations, we can att… view at source ↗
Figure 6
Figure 6. Figure 6: (Top left) Plot of the difference in the MAP χ 2 eff with respect to the ΛCDM model. The contours indicate the standard deviations for a χ 2 distribution with two degrees of freedom, corresponding to the expected distribution of ∆χ 2 = χ 2 w0wa − χ 2 Λ according to Wilks’ theorem (S. S. Wilks 1938). The contours are not applicable to QCD-DE since it is not a direct extension of ΛCDM. (Top right) Plot of th… view at source ↗
Figure 7
Figure 7. Figure 7: CMB T T and EE angular power spectra and their fractional differences relative to the best-fit ΛCDM model, ∆Cℓ/CΛCDM ℓ , computed at the MAP cosmological parameters for the CMB-SPA dataset (top panels) and the CM￾B-SPA+DD+DESI dataset combination (middle panels). (bottom panels) The fractional differences of all the power spectra above, relative to the MAP of ΛCDM for the CMB-SPA dataset [PITH_FULL_IMAGE:… view at source ↗
Figure 8
Figure 8. Figure 8: Residuals of the BAO distance indicators with respect to the MAP ΛCDM model for the CMB-SPA+DD+DESI dataset combination. The top, middle, and bottom panels show (DM/rd)/(DM/rd)ΛCDM, (DH/rd)/(DH/rd)ΛCDM, and (DV /rd)/(DV /rd)ΛCDM, respectively. in the transverse distance while still passing through the DESI measurements. In this sense, QCD-DE achieves a comparable fit to the data with a smaller departure fr… view at source ↗
read the original abstract

We investigate a physically motivated model of dynamical dark energy arising from the non-perturbative topological structure of the Quantum Chromodynamics (QCD) vacuum. Unlike conventional dark-energy scenarios, the model does not introduce any new fundamental field or propagating degree of freedom. Instead, the dark-energy density emerges as a global vacuum effect associated with the response of the QCD vacuum to an expanding spacetime, representing a possible paradigm shift in the interpretation of cosmic acceleration. We develop the first comprehensive cosmological implementation of this QCD-induced dark-energy scenario and confront it with current observations, including the latest combination of Planck, ACT and SPT-3G cosmic microwave background measurements, DESI DR2 baryon acoustic oscillation data, and Type Ia supernova samples from Pantheon+ and DES-Dovekie. We compare the model with both the standard $\Lambda$CDM cosmology and the widely used CPL ($w_0w_a$CDM) parametrization of evolving dark energy. We find that the model provides an excellent fit to the data and reproduces the late-time dark-energy evolution preferred by DESI observations. The inferred cosmological parameters are robust against different implementations of the dark-energy activation mechanism, indicating that the cosmological predictions are largely insensitive to the specific form of the transition. The model naturally predicts an effective phantom-crossing behaviour at intermediate redshifts while remaining free from the theoretical instabilities commonly associated with phantom scalar-field models. Using a combination of goodness-of-fit statistics and Bayesian model-selection techniques, including Akaike and Deviance Information Criteria and Bayesian evidence estimated from Markov Chain Monte Carlo chains, [abridged]

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a model in which dynamical dark energy arises as a global effect from the response of the QCD vacuum's non-perturbative topological structure to cosmic expansion, without introducing new fields or degrees of freedom. The authors implement this via a phenomenological activation mechanism whose functional form is varied, and show that the resulting cosmology provides an excellent fit to combined CMB (Planck+ACT+SPT-3G), BAO (DESI DR2), and SN (Pantheon+, DES-Dovekie) data, reproduces the DESI-preferred late-time evolution, predicts phantom-crossing without instabilities, and is robust to the activation choice. The model is compared to ΛCDM and CPL using AIC, DIC, and Bayesian evidence from MCMC.

Significance. If the central claim holds—that the dark-energy density emerges from QCD vacuum effects in response to expansion without new fields or ad-hoc tuning—this would constitute a significant advance by grounding evolving dark energy in established particle physics rather than new scalars or modified gravity. Strengths include the comprehensive dataset combination, explicit use of Bayesian evidence and information criteria for model comparison, and reported robustness of cosmological parameters to activation variations.

major comments (2)
  1. [implementation and activation mechanism section] The activation mechanism (varied across cases in the implementation section) is introduced and selected by hand to control the onset and time dependence of the vacuum response rather than obtained by solving the QCD vacuum (e.g., via instanton or gluon-condensate evolution) in a time-dependent FLRW metric. This makes the reproduction of the DESI-preferred w(z) evolution an input rather than an emergent, parameter-free prediction from QCD, directly affecting the central claim of a physically motivated, field-free model.
  2. [Abstract and results section] Abstract and results: no explicit posterior values, tension metrics (e.g., Δχ² or H0/S8 shifts relative to ΛCDM), or numerical Bayes factors are reported despite the use of MCMC chains and model-selection techniques; this weakens the quantitative support for the 'excellent fit' and 'robust' claims.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: [implementation and activation mechanism section] The activation mechanism (varied across cases in the implementation section) is introduced and selected by hand to control the onset and time dependence of the vacuum response rather than obtained by solving the QCD vacuum (e.g., via instanton or gluon-condensate evolution) in a time-dependent FLRW metric. This makes the reproduction of the DESI-preferred w(z) evolution an input rather than an emergent, parameter-free prediction from QCD, directly affecting the central claim of a physically motivated, field-free model.

    Authors: We agree that the activation mechanism is introduced phenomenologically rather than derived from a first-principles solution of the QCD vacuum in an expanding FLRW spacetime. A complete derivation from non-perturbative QCD would indeed be highly desirable but is currently beyond reach due to the complexity of solving the instanton or gluon condensate dynamics in a time-dependent metric. The present work focuses on implementing the global vacuum effect in cosmology and testing its viability against data. The fact that the results are robust across different activation forms suggests that the key features are not artifacts of the specific choice. We will revise the manuscript to more explicitly discuss this limitation and its implications for the physical motivation of the model. revision: partial

  2. Referee: [Abstract and results section] Abstract and results: no explicit posterior values, tension metrics (e.g., Δχ² or H0/S8 shifts relative to ΛCDM), or numerical Bayes factors are reported despite the use of MCMC chains and model-selection techniques; this weakens the quantitative support for the 'excellent fit' and 'robust' claims.

    Authors: The manuscript does report the use of AIC, DIC, and Bayesian evidence from MCMC, with detailed results in the main text and appendices. However, to enhance clarity and address this concern, we will add explicit numerical values for key quantities such as Δχ², parameter shifts, and Bayes factors to the abstract and include a summary table in the results section. revision: yes

standing simulated objections not resolved
  • The derivation of the activation mechanism from first-principles QCD in curved spacetime cannot be provided in this work, as it requires solving non-perturbative QCD dynamics in an FLRW background, which is not currently feasible.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper defines a QCD-vacuum-based dark-energy model, introduces an activation mechanism for its cosmological implementation, and reports that results are robust across different implementations of that mechanism while confronting the model with external datasets (Planck, DESI, supernovae). No quoted step shows a prediction or central result reducing by construction to a fitted input, self-citation, or ansatz whose functional form is the output itself. The derivation remains self-contained: the QCD motivation supplies the physical premise, the activation supplies a concrete implementation whose details do not dictate the reported data agreement, and model comparison is performed against independent observations and parametrizations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a QCD-vacuum response to expansion whose functional form is not derived from first-principles QCD but is instead parametrized and fitted. No new particles are introduced. The model inherits standard FLRW cosmology and the assumption that the QCD vacuum energy can be treated as a homogeneous background effect.

free parameters (1)
  • activation transition parameters
    Parameters controlling the redshift and sharpness of the vacuum-energy activation are introduced and varied; their values are chosen to match late-time data.
axioms (2)
  • domain assumption The QCD vacuum possesses a non-perturbative topological structure that can respond to spacetime expansion by generating a homogeneous energy density.
    Invoked in the opening paragraph of the abstract as the physical origin of the dark-energy density.
  • standard math Standard FLRW cosmology and linear perturbation theory remain valid when this vacuum energy is added.
    Implicit in the cosmological implementation and comparison to Planck/ACT/SPT data.

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discussion (0)

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