Evolving Dark Energy Is Vacuum Energy After All

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 $Λ$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]

• The paper demonstrates that cosmic acceleration emerges from the QCD vacuum's non-perturbative topological effects, eliminating the need for new dark energy fields.
• It introduces a QCD-induced dynamical dark energy model scaling as HΛ_QCD^3, validated through lattice simulations and modified Friedmann equations.
• Cosmological data, including CMB and BAO measurements, show that the model achieves a better statistical fit than ΛCDM while naturally addressing the coincidence problem.

QCD-Induced Dynamical Dark Energy: Vacuum Energy as the Driver of Cosmic Acceleration

Introduction and Physical Motivation

The cosmological constant problem, marked by the puzzling smallness and coincidence of the observed value of dark energy, continues to be a principal tension in theoretical physics. While $\Lambda$CDM remains compatible with high-precision cosmological datasets, current BAO and SNIa measurements, notably from DESI, hint at a deviation from a strict cosmological constant, with best-fit late-time expansion histories favoring evolving dark energy models. However, generic dynamical dark energy (DDE) scenarios typically require new light fundamental fields or modifications to gravitational physics, suffering from fine-tuning and theoretical instabilities.

"Evolving Dark Energy Is Vacuum Energy After All" (2606.20036) proposes a paradigm in which the observed cosmic acceleration emerges from a global vacuum response, specifically from the non-perturbative topological structure of the QCD vacuum in an expanding spacetime. This approach does not invoke new propagating degrees of freedom or additional potential energy sectors but interprets DE as a macroscopic quantum effect arising from QCD tunneling phenomena in curved backgrounds.

Theoretical Framework: QCD-Induced Vacuum Energy

The formalism is rooted in the distinction between the QCD vacuum energy in Minkowski space and in a curved, expanding spacetime (FLRW). The resultant energy density,

$$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$

is argued to scale as $\sim H \Lambda_{\rm QCD}^3$, where $H$ is the Hubble expansion rate and $\Lambda_{\rm QCD}$ is the intrinsic strong-interaction scale. This scaling is nontrivial: in contrast to standard intuition that QCD effects are ultraviolet and irrelevant at cosmological distances, the topological susceptibility of the QCD vacuum generates a non-dispersive, non-local component that remains sensitive to infrared scales due to finite-action tunneling events. This leads to a linearly $H$-dependent vacuum energy correction.

Lattice simulations and controlled computations in semi-realistic "deformed QCD" support the emergence of such linear corrections in the presence of large-scale topological effects, providing partial nonperturbative validation for this scaling. Implementing this prescription, the standard Friedmann equations are modified so that at late times, as the universe approaches a pure de Sitter attractor with constant $H$, the DE density asymptotes precisely to an effective cosmological constant of observed strength, set only by $\Lambda_{\rm QCD}$ and dimensionless QCD parameters.

Cosmological Model Construction

To yield a viable cosmology, the proposal introduces an activation function $\beta(z)$ to interpolate between negligible early-universe effects (when $H \gg \overline{H}$) and full QCD-DE at low $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$0 (late times). The function is engineered to ensure that the DE contribution is suppressed until the adiabatic condition,

$$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$1

is satisfied, i.e., only when the expansion rate is sufficiently slow and reminiscent of the late-time universe. The two switch parametrizations considered are

• $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$2
• $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$3

where $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$4 is a normalization, $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$5 defines the redshift of onset, and $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$6 defines the redshift interval across which DE activates. Both forms ensure a smooth, monotonic transition.

Figure 1: Switch function $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$7 and its derivative $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$8 for typical parameters, demonstrating the activation of the QCD-DE component around $$\rho_{\rm DE} = \varepsilon^{\rm vac}_{\rm FLRW} - \varepsilon^{\rm vac}_{\rm Mink},$$9.

Integrating the QCD vacuum response into the FLRW background, the Hubble rate is generalized to solve

$\sim H \Lambda_{\rm QCD}^3$0

so that all standard (early-time) cosmology is automatically recovered for $\sim H \Lambda_{\rm QCD}^3$1, and a de Sitter cosmology is approached for $\sim H \Lambda_{\rm QCD}^3$2. This construction ensures compatibility with all conventional constraints on Big Bang Nucleosynthesis, recombination, and structure formation.

Figure 2: Evolution of $\sim H \Lambda_{\rm QCD}^3$3, comparison of adiabaticity, and background evolution for QCD-DE and $\sim H \Lambda_{\rm QCD}^3$4CDM, illustrating a late-time transition to vacuum-dominated expansion.

Constraints from Cosmological Data

A comprehensive MCMC analysis is performed using combinations of CMB datasets (Planck, SPT-3G, ACT DR6), BAO measurements (DESI DR2), and SNIa (Pantheon+, DES-Dovekie). The QCD-DE model is compared not just to $\sim H \Lambda_{\rm QCD}^3$5CDM but to the Chevallier-Polarski-Linder parametrization ($\sim H \Lambda_{\rm QCD}^3$6CDM), the canonical two-parameter evolving dark energy description.

Key findings:

• Both QCD-DE parametrizations (exp and tanh) yield cosmological parameter posterior distributions remarkably close to $\sim H \Lambda_{\rm QCD}^3$7CDM, inducing a modest shift in $\sim H \Lambda_{\rm QCD}^3$8 to lower values and a slightly larger $\sim H \Lambda_{\rm QCD}^3$9.
• The activation redshift $H$0 is found to be $H$1, indicating DE's effective emergence at $H$2.
• The model remains statistically robust under the choice of SNIa sample or switch function $H$3.

  Figure 3: Joint posterior distributions comparing $H$4CDM, $H$5CDM, and QCD-DE, showing parameter degeneracies and allowed regions for $H$6 and $H$7.

The reconstructed QCD-DE equation of state manifests an effective phantom crossing at $H$8, notably earlier than the typical $H$9 favored by CPL-based DDE fits.

Figure 4: Posterior reconstruction of the effective QCD-DE equation of state from the CMB-SPA+DD+DESI combination, compared to the reference CPL behavior. The phantom crossing occurs at $\Lambda_{\rm QCD}$0.

Model Comparison and Statistical Evidence

The model's performance is evaluated with multiple statistical diagnostics: $\Lambda_{\rm QCD}$1, Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), and Bayesian evidence (Bayes factors, computed with the learned harmonic mean estimator). The results are substantially:

• QCD-DE matches $\Lambda_{\rm QCD}$2CDM in goodness-of-fit but consistently achieves a better trade-off between fit quality and parameter economy, being favored over $\Lambda_{\rm QCD}$3CDM in all full-dataset combinations.
• For the most stringent dataset (CMB-SPA+DD+DESI), QCD-DE attains a Bayes factor $\Lambda_{\rm QCD}$4 versus $\Lambda_{\rm QCD}$5CDM, compared to $\Lambda_{\rm QCD}$6 for CPL DDE, indicating moderate Bayesian preference.

Figure 5: Model comparison metrics ($\Lambda_{\rm QCD}$7, AIC, DIC, and Bayes factor) across datasets. QCD-DE is systematically favored over both $\Lambda_{\rm QCD}$8CDM and phenomenological DDE models in full combinations.

Additionally, QCD-DE predicts distinctive low-$\Lambda_{\rm QCD}$9 CMB temperature and polarization features, provides a better fit to the low-quadrupole $H$0 anomaly, and modifies the BAO residuals in a manner consistent with DESI's preferred expansion history.

Figure 6: CMB TT and EE angular power spectra and fractional residuals relative to best-fit $H$1CDM, highlighting the model's impact on low multipoles.

Figure 7: Residuals of BAO distance indicators relative to best-fit $H$2CDM, showing coherent late-time modifications in $H$3 and distance measures in the relevant redshift range.

Theoretical and Practical Implications

This framework delivers an economical, physically-motivated solution to the cosmic acceleration problem, qualifying as a testable, UV-complete alternative to scalar-field DDE, early dark energy, or modified gravity. Notably, the absence of additional propagating degrees of freedom circumvents generic pathologies such as instabilities (phantom crossing is permitted without gradient or ghost modes) and fine-tuned initial conditions.

Practically, the QCD-DE model is tightly linked to forthcoming cosmological probes:

• DESI and LSST will further scrutinize the expansion history at $H$4, the regime where QCD-DE effects activate.
• CMB-S4 and future polarization surveys can probe the predicted ISW and low-$H$5 modifications.

Theoretically, empirical evidence for such a vacuum effect would confirm the deep connection between cosmological-scale phenomena and nonperturbative QCD physics, lending support to the interplay of quantum anomalies, topology, and spacetime geometry.

Conclusion

The QCD-induced vacuum energy scenario robustly describes current cosmological observations without invoking new fields or nonminimal gravitational couplings. Through a non-local, topological QCD background effect, it naturally predicts evolving dark energy that transitions at $H$6 and provides fits to late-time data in line with empirical requirements, outperforming standard DDE parametrizations in Bayesian model comparison. The mechanism offers a theoretically consistent resolution to critical issues such as the coincidence and smallness problems, tracing the observed cosmic acceleration to Standard Model physics. This approach represents a compelling direction for further investigation as next-generation cosmological surveys deliver increasingly stringent constraints on the expansion history and the fundamental nature of dark energy (2606.20036).