DESI results and Dark Energy from QCD topological sectors

We present a physically motivated dark-energy (DE) model rooted in the topological structure of the Quantum ChromoDynamic (QCD) vacuum. In this framework, DE arises from the difference between the vacuum energy of an expanding FRW universe and Minkowski spacetime, induced by QCD topological sectors. The resulting DE term in the Friedmann equation scales with the Hubble rate, $ρ_{\rm DE}(t)\propto H(t)$, once DE dominates cosmic expansion, i.e. when the Universe is close to the de Sitter regime with $H\approx$ constant. The QCD scale, $Λ_{\rm QCD}\sim100~{\rm MeV}$, naturally fixes the DE density and explains why its influence becomes significant only recently. The construction relies solely on the Standard Model of particle physics, introducing no new fields or couplings. The most fundamental change is the possibility of modifying the evolution of the background cosmology in the Friedmann equation. Key predictions include: (a) A present-day equation of state parameter $w_{\rm DE,0}>-1$ that asymptotically approaches the de Sitter limit $w_{\rm DE}=-1$ in the future. (b) A present-day Hubble constant $H_0$ that asymptotically approaches a constant $\overline{H}$ set by $Λ_{\rm QCD}$. (b) For $z\ge 0$, $w_{\rm DE}(z)$ may lie above or below $-1$ and can cross this boundary multiple times at different $z$, behavior qualitatively consistent with the recent DESI findings. (c) In our framework, any deviation from $Λ$CDM leads to a corresponding deviation of $H(z)$, which can be tested with existing and future cosmological observations.

💡 Research Summary

The paper proposes a novel dark‑energy (DE) model in which the observed accelerated expansion of the Universe originates from the topological structure of the Quantum Chromodynamics (QCD) vacuum, without introducing any new fields or couplings beyond the Standard Model. The authors build on the 1967 Zeldovich prescription, which defines the gravitational vacuum energy as the difference between the vacuum energy computed in a curved (expanding FRW) spacetime and that in flat Minkowski space. Applying this to QCD, they argue that the non‑perturbative tunnelling between distinct topological sectors |k⟩ of the gauge theory generates a non‑local, long‑range contribution to the vacuum energy that is sensitive to the size of the universe, despite the presence of a mass gap.

Using analytic results obtained for a hyperbolic space H³_κ×S¹_κ⁻¹ and flat space R³×S¹, they show that the vacuum‑energy difference scales linearly with the curvature parameter κ: ΔE_vac ≈ c κ Λ_QCD³, where Λ_QCD≈100 MeV is the QCD confinement scale and c is an O(1) coefficient. By conjecturing that in a de Sitter‑like expanding universe the curvature κ is effectively replaced by the Hubble parameter H, they obtain ΔE_vac ∝ H Λ_QCD³. Consequently the dark‑energy density obeys ρ_DE ∝ H, a striking departure from the constant Λ of ΛCDM.

This scaling naturally yields the observed DE density because Λ_QCD³ ≈ (10⁻³ eV)⁴, matching the measured ρ_DE ≈ (2 meV)⁴ without fine‑tuning. Moreover, the Friedmann equation modified by ρ_DE∝H predicts that as the Universe approaches a de Sitter state, H tends to a constant value set by Λ_QCD, and the equation‑of‑state parameter w_DE asymptotically approaches –1. However, during the transition era w_DE can deviate from –1, cross the phantom divide multiple times, and even become greater than –1, reproducing the redshift‑dependent behavior reported by the recent DESI collaboration (w_DE(z) > –1 today but w_DE(z>0) < –1 at higher redshift). The model therefore accommodates the “quintom‑like” evolution without invoking a dynamical scalar field, avoiding the instabilities (negative sound‑speed squared, unitarity violation) that plague conventional phantom or quintom constructions.

The authors emphasize that the effect is intrinsically non‑perturbative (∝ exp(–1/g²)) and non‑local; it cannot be captured by any local effective field theory. They draw analogies to the Aharonov‑Casher effect, ’t Hooft’s infrared cutoff in instanton calculus, Lüscher’s long‑range force in gauge theories with instantons, and the Veneziano ghost, all of which illustrate how topological configurations can generate power‑law finite‑size corrections despite a mass gap. Lattice studies of “deformed QCD” and analytic calculations in weakly coupled deformed models support the linear L⁻¹ dependence, reinforcing the plausibility of the linear H term in the cosmological context.

Observationally, the model makes two clear predictions: (1) the Hubble parameter H(z) will deviate from the ΛCDM curve in a way directly correlated with any deviation of w_DE(z) from –1, because ρ_DE∝H; (2) the equation‑of‑state will cross w=–1 several times as a function of redshift, a signature that can be probed by upcoming large‑scale structure surveys, supernovae, and BAO measurements. Confirmation of these signatures would provide strong evidence that the QCD vacuum’s topological sectors are responsible for dark energy, representing a profound link between low‑energy strong‑interaction physics and cosmology.

In summary, the paper offers a compelling, Standard‑Model‑based mechanism for dark energy rooted in QCD topology, explains the observed magnitude of DE, predicts a dynamical w_DE(z) consistent with DESI results, and outlines concrete observational tests. If validated, this framework would resolve the dark‑energy puzzle without invoking exotic fields, while simultaneously revealing a deep, previously hidden cosmological role for QCD’s topological structure.