This manuscript derives the cosmological consequences of modeling the vacuum as a relativistic logarithmic superfluid. We demonstrate that the logarithmic equation of state yields a barotropic parameter of w = -1 natively, identifying dark energy not as an exotic additional cosmological component, but simply as the intrinsic thermodynamic pressure of the vacuum condensate itself. By combining the emergent gravitational coupling Geff ~ c²/(ξ²ρ₀) with the observed empirical relation Ωγ ≈ α², we derive a fundamental vacuum self-consistency equation. This equation mathematically links the fine structure constant, the Hubble parameter, the vacuum mass density, and the CMB photon energy density into a single unified framework. Crucially, this framework predicts that when the vacuum density varies spatially, the local speed of light (cs), the gravitational constant (G), and the effective cosmological constant (Λ) must all vary together in calculable ways governed exactly by the equation of state. Applying this to local large-scale structure, we show that a modest ~3.6% vacuum underdensity inside the observed KBC void is sufficient to produce the locally measured Hubble constant of H₀ ≈ 73 km s⁻¹ Mpc⁻¹ from a global background value of H₀ = 68.15 km s⁻¹ Mpc⁻¹, thereby naturally resolving the Hubble tension. Finally, we prove that the CMB acoustic peak positions remain exactly invariant under these local parameter variations, because both the sound horizon and the comoving distance scale linearly with the local speed of light. The framework thus automatically satisfies the most stringent early-universe cosmological bounds while simultaneously resolving late-universe observational tensions.
Benny Boris Kulangiev (Sat,) studied this question.