Vacuum Elastodynamics: Resolving the Hubble and S8 Tensions via Lattice Viscosity and Phantom Dark Energy

We present Vacuum Elastodynamics, a unified geometric framework that resolves the “Crisis of Consistency” in cosmology by modeling the vacuum not as an empty void, but as a Hyperuniform E8 Supersolid crystallizing at the Planck scale. We propose that the universe is currently undergoing a “stiffness phase transition” at redshift z ≈ 0.65, identified geometrically as the site percolation threshold (pc ≈ 0.31) of the vacuum lattice. This relaxation releases elastic energy, boosting the late-time expansion rate to alleviate the Hubble Tension. By enforcing the Lepton Sum Rule, we find an effective viscosity of η ≈ 0.1569 (consistent with the Lepton Sum Rule) operating within a theoretical stability limit of ηmax ≈ 0.21 derived via the Fluctuation-Dissipation Theorem. This stiffer vacuum predicts a local Hubble constant of H0 ≈ 74.5 km s−1 Mpc−1, which is fully consistent with SH0ES measurements (73.0 ± 1.0) within observational errors. Crucially, the dynamic viscosity cascade—transitioning from a jamming peak (η ≈ 0.31) to the observed proton load (η ≈ 0.1569)—suppresses structure formation to S8 ≈ 0.776. This fully Resolves the tension with Weak Lensing surveys without requiring viscosity to exceed the observed constraints [7–9]. We demonstrate that this mechanism preserves early-universe physics via a "Cancellation Theorem,” where the geometric scaling of particle masses (m ∝ G−0.5) and cross- sections ensures the invariance of Big Bang Nucleosynthesis abundances and the CMB acoustic scale (verified to < 0.1% precision). Furthermore, the enhanced gravity of the early vacuum (Gearly ≈ 1.22G0) acts as a “Cosmic Turbocharger,” accelerating halo assembly to explain the massive high-redshift galaxies observed by JWST. Finally, we identify “Phantom” Dark Energy (w ≈ −1.034) as the viscous drag of matter against the expanding lattice. A global Bayesian analysis across Planck, Pantheon+, and BAO data reveals that the vacuum relaxation model resolves the absolute magnitude calibration Tension (∆χ 2 ≈ −3566.6 relative to the Planck-calibrated baseline) while maintaining statistical indistinguishability from the optimized supernova expansion history (∆χ 2 ≈ −0.6). The framework offers a falsifiable geometric origin for the fundamental constants, identifying the fine-structure constant (α −1 ≈ 137) and the generation limit (N = 3) with the topology of the underlying fiber bundle.