Dynamic Substrate Cosmology — Viscoelastic Vacua, Galaxy Rotation without Cold Dark Matter, and Acoustic Horizon Analogues

Abstract Modern cosmology faces severe phenomenological challenges, including the mandatory introduction of unobserved Cold Dark Matter (CDM) and fine-tuned Dark Energy components, alongside the persistence of initial cosmological singularities. This work applies the Dynamic Substrate Theory (DST) to large-scale cosmic evolution, galaxy rotation curves, gravitational wave dispersion, and laboratory analogues. From substrate conservation equations under Maxwell-Oldroyd-B rheology, we derive modified Friedmann expansion dynamics where late-time cosmic acceleration arises dynamically from elastic strain relaxation. Furthermore, by incorporating long-range vacuum shear rigidity (\mu_{\text{shear}}) into the modified Poisson equation, we naturally reproduce flat asymptotic rotation velocities (v_{\infty} = \text{const}) in galactic outskirts without invoking invisible dark matter halos. Finally, we establish high-frequency gravitational wave dispersion relations and propose superfluid laboratory analogues to validate the hydrodynamic properties of the vacuum substrate. Keywords: Viscoelastic Cosmology, Dark Matter Alternatives, Galactic Rotation Curves, Gravitational Wave Dispersion, Analogue Gravity.