DESI results and Dark Energy from QCD topological sectors

The gist The authors present a physically motivated dark-energy (DE) model rooted in the topological structure of the Quantum ChromoDynamic (QCD) vacuum, where DE arises from tunnelling transitions between QCD topological sectors, which offers a framework free from issues associated with dynamical scalar fields.

How it works

1. DE is identified with the vacuum energy produced by tunnelling transitions between different topological sectors in an expanding universe, following the subtraction of a large contribution computed in Minkowski spacetime, an approach known as the Zeldovich prescription Y. B. Zhitnitsky (1967). The amplitude of DE is determined by the QCD energy scale, as given in Eq. (3), while its time dependence arises from the evolution of the topological sectors k⟩ and the corresponding variation in tunnelling transition rates in an expanding universe

2. The framework relies on non-perturbative computations in QCD, where tunneling transitions are described using classical solutions such as instantons, calorons, and similar configurations

3. The vacuum energy difference between the relativistic hyperbolic spacetime H3κ × S1κ−1 and flat Minkowski spacetime is given by a linear correction proportional to κ, i.e., ∆Evac ≡ Evac[H3κ × S1κ−1] − Evac[R3 × S1] ≈ (1) − Λ4QCD 1 − cκ/ΛQCD - Λ4QCD ≈ cκκ · Λ3QCD, where numerical factors are omitted and cκ is a dimensionless numerical coefficient of order one

Key Predictions and Implications

The paper outlines several key predictions stemming from this QCD-induced DE mechanism:

(a) A present-day equation of state parameter wDE,0 > −1 that asymptotically approaches the de Sitter limit wDE = −1 in the future.

(b) A present-day Hubble constant H0 that asymptotically approaches a constant H set by ΛQCD.

(c) For z ≥ 0, wDE(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.

(d) In our framework, any deviation from ΛCDM leads to a corresponding deviation of H(z), which can be tested with existing and future cosmological observations.

Cosmological Behavior in de Sitter and Expanding Universes

The pure de Sitter state can be characterized by a single parameter—the Hubble constant H—and the tunnelling transitions in QCD generate dark energy with the same characteristics as a cosmological constant, as given by (6) and its equation of state (7). The resulting equation of state assumes the form w = PDE/ρDE = −1, a(t) ∝ exp(Ht), which is precisely the behaviour describing the de Sitter Universe. In contrast, as we approach the present time, when x(t0) ∼ 1, Eq.(16) yields w ≃ −0.7, illustrating two important consequences of our framework: (1) the equation-of-state parameter w is time-dependent, and (2) it is indeed possible to have w > −1 at the present epoch.

Phenomenological Implementation and Testability

To account for deviations from exact de Sitter behavior for z ≥ 0, a time-dependent activation function β(t) is introduced such that the DE density is parameterized as ρDE = β(t)cHΛ3QCDH, where β(t) ∈ (0, 1). This function serves as a switch that activates dark energy at a certain redshift, and it can be interpreted as a physically motivated parametrization of dark energy within our framework. The main result of this numerical experiment is that it is straightforward to obtain an equation of state parameter that varies with time and can take values both above and below −1 without the need for a new dynamical field. Furthermore, the correlation between the Hubble parameter H(z) and w(z) is unique to our framework because it comes from the fact that ρDE(t) ∝ β(t)H(t) in recent times when DE started to dominate the evolution of the universe.

Connection to Cosmological Tensions

The framework suggests a unique connection between wDE(z) and H(z), providing a distinctive, testable prediction that may offer a natural explanation for the observed tension between the local measurement of the Hubble constant H0 and its value inferred from observations at z ∼ 1100. The modification of the Friedmann equation at all redshifts, determined by the unknown function β(z), allows comoving distances to be altered across the entire redshift range, paralleling the evolution of the Hubble constant shown in Panel (a) of Fig. 2. This behavior parallels how clustered dark energy or a dark-energy equation of state that correlates with local mass density can emerge without introducing any exotic additional fields.

Conclusion and Future Directions

The QCD-induced dark energy model offers a natural resolution to several long-standing fine-tuning problems, including the “coincidence problem,” the “drastic separation of scales,” and the “unnatural weakness of interactions”. The key new element introduced in this work is the extension of earlier ideas to account for deviations from a pure de Sitter state, fully motivated by recent DESI results. The framework predicts that wDE may lie above or below −1 and can cross the w = −1 boundary multiple times throughout the history of the Universe, a trend suggested by the DESI results. The ultimate answer regarding tabletop experiments is affirmative, as this represents a genuine physical phenomenon rather than a mere formal reinterpretation of equations.

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The final remark concerning possible future developments of this work is as follows. It is well known that de Sitter–like behavior has occurred twice in the history of the Universe: first during the inflationary epoch, and again in the present epoch dominated by dark energy. The dark energy framework explored in this paper may offer valuable insights into the inflationary phase. Indeed, in a purely hypothetical scenario proposed in A. R. Zhitnitsky (2014); A. O. Barvinsky & A. R. Zhitnitsky (2018), the vacuum energy responsible for inflation could also arise from tunnelling transitions in a novel, as yet unidentified, strongly coupled gauge theory—an idea analogous to the QCD-based mechanism we advocate here for generating the dark energy scale, as described in Eq. (3).

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It turns out that these topological fields exhibit precisely the properties of the Veneziano ghost G. Veneziano (1979), which was originally postulated to resolve the so-called U(1)A problem in QCD. This connection between dark energy and the Veneziano ghost, as originally proposed in F. R. Urban & A. R. Zhitnitsky (2010a,b), led to the model being named “Ghost Dark Energy” (GDE). Crucially, this field does not propagate and does not violate any fundamental principles of quantum field theory, as clarified in Appendix A. The computation of a speed of sound in this context is meaningless, as there is no physical field to support fluctuations.

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The linear correction ∼ κ in ∆Evac can be traced, at a technical level, to the differing behavior of monopole configurations at large distances in the two backgrounds

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In this Appendix we want to generalize the results of ref. F. R. Urban & A. R. Zhitnitsky (2009) for time dependent perturbation with the main objective to test the adiabatic condition (17) using a simple exactly solvable 2d QED. The correspondence between 2d QED and physical case (17) is as follows mγ → ΛQCD, L˙ → H˙/H2, ∆t → H−1, L−1 → H. In this case the correction to Minkowski value (proportional to [H · Λ−1QCD]) and which is identified with the QCD-DE, assumes the form ∆E2d ∝ 1/mγ(L + L˙ ∆t) ⇒ ρDE ∝ HΛQCD / h1 + H˙HH i.

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The basic outcome of these studies from Appendix C is that the qualitative arguments presented above on suppression due to time dependent perturbation are indeed accurate. The main result of this numerical experiment is that it is straightforward to obtain an equation of state parameter that varies with time and can take values both above and below −1 without the need for a new dynamical field.

1. textbfImprove cosmological model parameter estimation by incorporating QCD vacuum structure as a fundamental constraint on dark energy evolution. The improved AI can perform a full statistical analysis using a realistic parametrization of β(z) to determine which activation function, such as β1(t) or β2(t), best fits current observational constraints from CMB, BAO, SN, and LSS data (Figure 3).

2. textbfEnable cross-correlation analysis between Hubble parameter and dark energy equation of state. The system can exploit the unique connection between wDE(z) and the Hubble parameter H(z) to test the distinctive, testable prediction that arises from ρDE(t) ∝ β(t)H(t), providing a new avenue for dark energy coupled to the dark sector.

3. textbfDetect deviations from quintessence models by systematically evaluating the consistency of phantom behavior in QCD-induced DE. The AI can perform a comprehensive analysis to determine if the observed crossing of the w = −1 boundary, as suggested by DESI results, is consistent with the fundamental principles of quantum field theory because it is not in terms of any new dynamical field.

4. textbfIdentify potential resolution for the H0 tension via time-dependent cosmological parameters. The system can explore how a function β(z) can alter comoving distances across the entire redshift range, potentially offering a path to reconcile the discrepancy between local and early-universe Hubble constant measurements, as suggested by Panel (a) in Fig.2.

5. textbf Assess the empirical testability of topological effects via tabletop experiments. The AI can evaluate proposals for detecting the Topological Casimir Effect by checking if it is possible to detect a novel contribution to the Casimir vacuum energy in Maxwell theory, providing a direct empirical support for the model's origin in tunnelling processes between different topological sectors.