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

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 $E_{8}$ Supersolid crystallizing at the Planck scale. We propose that the universe initiated a “Vacuum Phase Transition” at redshift $z \approx 0.65$, identified geometrically as the site percolation threshold ($p_{c} \approx 0.31$) of the vacuum lattice. This relaxation releases elastic energy, boosting the late-time expansion rate to alleviate the Hubble Tension. Global expansion is constrained by the macroscopic Geometric Yield Strength ($\eta_{max} \approx 0.21$), derived via the Fluctuation-Dissipation Theorem. This stiffened vacuum trajectory predicts a local Hubble constant of $H_{0} \approx 74.5$ km s$^{-1}$ Mpc$^{-1}$, fully consistent with SH0ES measurements ($73.0 \pm 1.0$) within observational errors. Crucially, the dynamic viscosity settles to a local effective value of $\eta_{sat} \approx 0.1569$. This value is structurally valid because it saturates 98.6% of the microscopic Frenkel Yield Strength ($\gamma_{crit} \approx 0.159$), thereby strictly forbidding a 4th lepton generation while ensuring stability. This specific viscosity suppresses structure formation to $S_{8} \approx 0.776$, fully resolving the tension with Weak Lensing surveys without exceeding observed constraints. We demonstrate that this mechanism preserves early-universe physics via a “Cancellation Theorem,” where the geometric scaling of particle masses ($m \propto G^{-0.5}$) 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 ($G_{early} \approx 1.22G_{0}$) acts as a “Cosmic Turbocharger,” accelerating halo assembly to explain the massive high-redshift galaxies observed by JWST. Finally, we identify “Phantom” Dark Energy ($w \approx -1.036$) 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 ($\Delta\chi^{2} \approx -3577.6$ relative to the Planck-calibrated baseline) while maintaining statistical indistinguishability from the optimized supernova expansion history ($\Delta\chi^{2} \approx 0.28$). The framework offers a falsifiable geometric origin for the fundamental constants, identifying the fine-structure constant ($\alpha^{-1} \approx 137$) and the generation limit ($N = 3$) with the topology of the underlying fiber bundle.