Cosmological Implications of the Logarithmic Superfluid Vacuum: Dark Energy, the Hubble Tension, and a Vacuum Self-Consistency Equation

Abstract

This version reworks the cosmology, mainly around the Hubble tension and dark energy. The earlier version explained the tension through a modified local expansion rate, with the effective cosmological constant scaling as the fourth power of the local light speed. That scaling doesn't survive a careful treatment. Writing the local Friedmann equation with every constant at its local value, the dark-energy term turns out to be exactly invariant under changes in vacuum density — the gravitational coupling and the vacuum pressure carry opposite powers that cancel. So local density variations can't move the expansion rate through the dark-energy channel. The tension is instead a matter-sector effect. Our distance-ladder anchors sit inside the Keenan-Barger-Cowie void, which has less matter, decelerates less, and so expands faster than the cosmic mean. Standard growth dynamics give the excess as −(1/3)f·δ_m; at the void's measured contrast (−20% to −46%), this spans the observed 73/68 ratio, with −41% hitting it exactly. The two Hubble values are two real local expansion rates, and the magnitude follows from the measured underdensity with no free parameter. Because our vacuum is a superfluid rather than an empty metric, there's an extra push absent in ordinary void models: a matter-poor region has fewer sinks draining it, so the condensate flows outward, adding to the expansion with the same sign. The signature is a decline of the inferred H₀ as the sample reaches past the void. Dark energy is also handled better. The sound-speed pole sits right next to the background density, so the vacuum can't drift by cosmological factors without leaving the physical branch. The density is pinned, the pressure with it, and the framework derives a genuine cosmological constant rather than assuming one — along with the constancy of the speed of light over cosmic time. The cosmological-constant-problem section is rewritten around this: the Planck-scale background doesn't gravitate through its magnitude, only its pressure enters the Friedmann equation, and the 120-order gap is a comparison between two quantities playing different roles. The CMB peak-invariance theorem, the parameter-free CMB temperature prediction (matching FIRAS to 28 ppm), and the T(z) = T₀(1+z) derivation are unchanged. Citations to the retracted dark-matter companion are removed, and the earlier equation-of-state and sign errors are fixed throughout.