Dilatant Dark Fluid: Toward a Unified Dark-Sector Foundation of Lorentz Invariance, Gravity, and Cosmological Phenomenology

This work introduces a cold-dark-matter substrate with two coupled components: an ultralight superfluid scalar sector \(\phi\) and a dispersed sector \(\varphi\) of heavier bosons, respectively acting as the continuous and dispersed phases of a dilatant dark fluid (DDF). Under shear stress, the dispersed phase undergoes collective jamming: the resulting velocity-dependent shear-thickening response yields the Lorentz factor as the jamming factor of the DDF. In this picture, the speed of light is the speed of transverse phonons in the saturated stiff limit of the DDF, a limit accessible to transverse excitations but not to massive bodies. Consequently, it is shown that relativistic kinematics, Lorentz invariance, and the associated null results of invariance tests can emerge from the medium's dilatant response rather than from independent spacetime postulates. The large masses of celestial bodies make dissipative accelerations negligible over gigayear timescales, while a conservative elastic-sheath response at the body-DDF interface accounts for perihelion precession. Massive particles are modeled as quantized vortices within the superfluid, where circulation structure gives spin and the Bernoulli pressure deficit manifests as the gravitational field. Solutions of Einstein's field equations are read in Painlevé-Gullstrand variables as emergent quantum-hydrodynamic phenomena rooted in the dark substrate. Weak-field gravitational phenomenology is recovered through Bernoulli pressure gradients in the DDF; strong-field sectors are reframed through the same DDF constitutive dynamics, with LVK-class transients described as shear-jammed \(\varphi\) transport. A MOND-like outer-galaxy regime is driven by isothermality of the superfluid phase. Cosmological redshift becomes a coherent, achromatic energy transfer to the background, different from earlier tired-light variants based on incoherent photon scattering; large-scale structure is attributed to the same characteristic vortex-filament morphology observed in doped superfluids, with predicted filament spin; BAO-like correlations arise from the mean-vortex-spacing scale of the vortex-filament web; and the CMB is identified with the medium's thermal equilibrium radiation. Full CMB transfer calculations and statistically complete cosmological comparisons are left for subsequent work. The result is a comprehensive proposal for a unified dark-sector account of Lorentz invariance, gravity, and cosmological phenomenology, distinct from earlier superfluid-vacuum and emergent-spacetime approaches, yielding explicit empirical discriminants.