This preprint presents the Sovereign Scaling Resonance (SSR) model — a pseudo-scalar dark energy field governed by a cosine potential whose vacuum scale is anchored to the Planck–proton mass-ratio hierarchy. The oscillatory equation of state w (z) ≈ −1 + A·sinω·ln (1+z) + φ is derived analytically from the field action via WKB treatment, not postulated. The shift symmetry of the cosine potential mandates an axion–photon coupling by standard effective field theory, connecting the cosmological model to near-future laboratory experiments. Key results: MCMC constraints (259, 870 steps, R−1 = 0. 011): H₀ = 70. 76 ± 0. 87 km/s/Mpc, Ωₘ = 0. 2715, A = 0. 031, ω = 5. 40 ± 0. 70, fM = 0. 503 ± 0. 32 Mₚl S8 amplitude tension improvement: Δχ²growth = −22. 11 (driven by KiDS-1000 and DES Y3 S8 priors) Full perturbation-level Boltzmann (PPF, cs²=1): σ₈ = 0. 763, S₈ = 0. 726, ISW RMS = 0. 34% over ℓ = 2–30, P (k) enhancement ~0. 6% at all scales — all deviations below Planck detection threshold Field mass m_Ξ ≈ 5 meV (68% CI: 3–13 meV) falls in the CAST-IAXO and PVLAS-FIN target range ΔBIC = +48. 6 (honest range +21 to +48. 6 after effective degrees-of-freedom correction) Non-oscillatory Gₑff comparator run explicitly: constant suppression (1 param, ΔBIC = +6. 3) achieves comparable S8 improvement; oscillatory structure distinguishable with Euclid DR1 (~2027) at ~12–25σ via weak lensing DESI w₀-wₐ tension quantified: SSR CPL projection (w₀ = −1. 030, wₐ = +0. 070) sits 4. 1σ from DESI DR1 best fit; ΛCDM sits 3. 7σ; both models comparably inconsistent with the DESI signal Gravitational instanton check: flat-space, Coleman–De Luccia, and Hawking–Moss analyses all yield actions ~10¹¹⁶⁻¹¹⁸, confirming Sᵢnst ≈ 22 is a numerical observation of the QCD–Planck hierarchy, not a derived instanton action WKB validation: adiabaticity ratio confirmed numerically at 8×10⁻⁴ — 30 times smaller than the conservative analytical bound fσ₈ compilation robustness: shape-only Δχ² ∈ −0. 03, +0. 02 across Nesseris, Sagredo, and Avila compilations — S8-prior driven and compilation-independent UV completion: unified KKLT construction (τₛ = 3. 501, V₆ ~ ζ³, three-axion KNP chain a=1, b=6) simultaneously satisfies ρSSR = Mₚl⁴/ζ⁶, Sᵢnst = 22. 00, and fₑff = 0. 517 Mₚl within MCMC 1σ, with tadpole = 37 ≪ 500; moduli stability verified (Hessian positive-definite, W₀ = − (1+Sᵢnst) e^−Sᵢnst determined by Sᵢnst=22 alone) ; holographic AdS/CFT gives fM naturally with RAdS/lₛ = 1. 78; topological index reframes ρSSR as geometric necessity; QCD instanton packing fraction 1/f = 71–124 provides candidate mechanism for vacuum energy suppression Stability checks: phase φ covers 51% of the 2π cycle (not fine-tuned) ; isocurvature bound Hᵢnf ≲ 1. 7×10¹⁴ GeV satisfied; neutrino degeneracy broken by scale-independence (λC ≈ 39 μm) ; cosmic birefringence gₐγγ ≲ 0. 070 satisfied; CMB lensing unbiased; BBN unaffected; parametric resonance absent (Mathieu ratio 1, 559) Nested sampling Bayes factor: run in progress (log Z (SSR) = −25. 13 at 68% remainder, log Z (ΛCDM) = −30. 69 complete; partial log B = +5. 56 in favour of SSR — final result pending) Data and code: MCMC chains and analysis pipeline available at doi: 10. 5281/zenodo. 20260778 and github. com/impulsiveaura/ssr-dark-energy The current evidence state is best characterised as "interesting and worth pursuing": the model makes genuine theoretical contributions but does not yet compel preference over ΛCDM. Decisive experimental tests are expected within ~5 years via CAST-IAXO, Euclid, and DESI Year 5.
Sharaf Samiur Rahman (Sun,) studied this question.