Quantum Gravity and String Theory

A Minimal Superfluid Vacuum Model with Global Mismatch: Vacuum-Energy Suppression, Hierarchy Resolution, Emergent Gravity, and an Independent Derivation of the Condensate Mass

Authors: Jon Caldwell

A single quantum superfluid condensate with no free parameters is proposed as the physical vacuum. The dimensionless over-capacity mismatch ε is not a free in put; it is derived from the CW—BCS self-consistency condition (Sec. 2.5.5), ε = k2 max,C/(2π2mln(kmax,C/kmax,IR)) = 0.1452; the numerical approximation ε ≈ 0.15 (accurate to 3%) coincides with the two-loop value for the derived coefficient c2 = −6(from the O(2) two-loop beta function), so all numerical results already operate at twoloop precision. Two competing nonlinear terms—quartic and logarithmic—produce twoindependent coherence scales: an IR scale suppressing vacuum energy (kIR = 8meV) anda UV scale regulating the Higgs self-energy (kUV ≈ 348GeV). The condensate effectivemass is derived with no free parameters from the logarithmic Gross—Pitaevskii phonondispersion and the GW170817 constraint cs → c, giving m ≈ 40meV/c2. The hierarchy ratio γ/(gρ0) = 5.77 × 10−8 is expressed as a closed formula in observational inputs,shown to be technically natural by ’t Hooft’s criterion, and shown to be structurallygenerated by one-loop Coleman—Weinberg corrections. The ratio kmax,C/kmax,IR = 90is derived by dimensional transmutation: the CW—BCS self-consistency condition determines λrel = 4/ln(kmax,C/kmax,IR) = 0.8895, and the gap equation kmax,C/kmax,IR =exp(Npair/λrel) with Npair = 4 reproduces the observed ratio exactly at one loop. Nofree parameter is introduced. Quantitative fits to SPARC rotation curves (UGC 128:χ2/dof = 1.00; NGC 3198: χ2/dof = 2.25) with ε fixed determine the vacuum referencedensity ρ0 ≈ 2.56×1032kgm−3 and the observer correction β = 1.60×10−48 from a singlefit, with 0.7% consistency between the two galaxies. The emergent gravitational metricsatisfies γPPN = +1 (Cassini bound satisfied; residual δγ ∼ 10−24). The CMB first peakℓ1 = 220 is reproduced as a consistency statement: the condensate is pressureless (w → 0) at CMB scales and encodes the same matter/energy content as ΛCDM. The sharpestnear-term test is an oscillatory Casimir force deviation (amplitude ∼ 0.18% at d = 1µm;period ℓwall = 0.275µm) with a material-dependent phase shift of ∆ϕAu→Ag ≈ 0.07rad(3nm plate-separation offset) that is parameter-free.

Comments: 34 pages. AI-assisted development of a superfluid vacuum model with zero free parameters. All physics verified by the author. Contemporaneous with Zenodo preprint DOI: 10.5281/zenodo.19169701

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[v1] 2026-03-23 01:15:16

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