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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19017167 |
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- <p> </p> <p><strong> </strong><strong>Paper #3a in the research program "What If the Vacuum Gravitates Locally?"</strong></p> <p><strong>Programme context.</strong> This 17-paper programme investigates the hypothesis that quantum vacuum energy and the cosmological constant are physically distinct, with the vacuum responding to local matter density through ρ_vac(ρ_m) = Λ₀ − α ρ_m. Paper #3 derived this functional form from one-loop QFT in curved spacetime but found a 10³² gap between the perturbative coefficient (α ~ 10⁻³⁴, gravitationally suppressed) and the phenomenological requirement (α ~ 10⁻³). Paper #8 established the observational constraints from structure growth data. Paper #9 discovered an unexpected nonlinear self-screening in N-body simulations.</p> <p><strong>What this paper does.</strong> Paper #3a closes the 10³² gap. The derivation uses finite-density QCD — the standard framework for nuclear matter — rather than quantum gravity. Three standard, experimentally verified ingredients are combined:</p> <ol> <li>The Gell-Mann–Oakes–Renner relation (tested to ~5%).</li> <li>The in-medium chiral condensate shift at finite baryon density (Drukarev & Levin 1991, Cohen et al. 1992).</li> <li>The nucleon sigma terms σ_π ≈ 50 MeV and σ_s ≈ 40 MeV (measured in πN scattering and on the lattice).</li> </ol> <p>The result: α = (σ_π + σ_s)/m_N ≈ 0.096. No new physics is invoked.</p> <p><strong>The equation-of-state argument.</strong> The chiral condensate ⟨q̄q⟩ is a Lorentz scalar. Its energy therefore has stress-energy T^μν ∝ g^μν, giving equation of state w = −1 exactly. This is vacuum energy in the precise general-relativistic sense — distinguished from ordinary matter (w = 0) by Lorentz structure, not by convention.</p> <p><strong>The strangeness sigma term.</strong> σ_s ≈ 40 MeV measures the nucleon's coupling to virtual s̄s pairs in the QCD vacuum. Strange quarks are not valence constituents of the nucleon — they exist only as vacuum fluctuations. This is an unambiguous vacuum effect with no separation ambiguity, providing a model-independent lower bound α_s = σ_s/m_N ≈ 0.04.</p> <p><strong>The factor-of-1.7 agreement.</strong> Two physical reduction factors bring the bare QCD prediction into agreement with observations:</p> <ul> <li>Dark matter does not carry color charge → only baryons couple → ×(Ω_b/Ω_m) = ×0.156</li> <li>Nonlinear screening from Paper #9 → ÷3</li> </ul> <p>Result: <strong>α_predicted = 0.005</strong>. Paper #8 best fit: <strong>α_observed = 0.003</strong>. Ratio: <strong>1.7</strong>. No free parameters.</p> <p><strong>Position within the programme.</strong> If this derivation holds, it transforms the gravitating vacuum model from a phenomenological ansatz into a consequence of QCD. The coupling α is no longer a free parameter — it is determined by measured sigma terms, the Planck baryon fraction, and the nonlinear screening from N-body simulations. Paper #3a is the theoretical foundation; Papers #8–#9 provide the observational and computational verification.</p> <p><strong>Programme links:</strong></p> <ul> <li>Full programme page: <a href="https://interdisciplinary-research.institute/2026/03/11/research-program-invitation/">https://interdisciplinary-research.institute/2026/03/11/research-program-invitation/</a></li> <li>Paper #8 (Structure Growth): <a href="https://www.researchgate.net/publication/401979975">https://www.researchgate.net/publication/401979975</a></li> <li>Paper #9 (N-body Simulations): <a href="https://www.researchgate.net/publication/401992447">https://www.researchgate.net/publication/401992447</a></li> </ul> <p>Recommended for submission to <em>Foundations of Physics</em>.</p> <p><strong>Author:</strong> Boris Kriger ORCID: 0009-0001-0034-2903</p> <p><strong>Affiliations:</strong></p> <ol> <li>Information Physics Institute, Department of Theoretical Astrophysics and Cosmology</li> <li>Institute of Integrative and Interdisciplinary Research, Toronto</li> </ol> <p><strong>Upload type:</strong> Preprint <strong>License:</strong> CC BY 4.0</p> <p><strong>Keywords:</strong> vacuum energy, sigma term, chiral condensate, finite-density QCD, vacuum–matter coupling, equation of state, cosmological constant, dark energy, trace anomaly, S8 tension, running vacuum model</p>