Dilatant Dark Fluid: Toward a Unified Quantum-Hydrodynamic Origin of Lorentz Invariance, Gravity, and Cosmological Phenomenology

This work introduces the dilatant dark fluid (DDF), a pervasive cosmic cold dark medium comprising two coupled ultralight bosonic sectors: a superfluid \(\phi\) and a heavier dispersed phase \(\varphi\) undergoing stress-induced shear jamming, distinguishing the framework from earlier superfluid-vacuum models. The DDF's velocity-dependent dilatant response drives the local \(\varphi\) sector toward a saturated jammed state that supports the propagation at \(c\) of coupled transverse phonons identified with photons, while remaining asymptotically inaccessible to massive bodies. This constitutive response generates a jamming factor identical to the Lorentz factor, recovering Lorentz-form kinetic energy, clock rate, and length relations, alongside interferometric and resonator nulls. By governing both matter dynamics andoperational measurement standards, the DDF provides a quantum-hydrodynamic material realization of geometric relativistic spacetime. The superfluid sector supports quantized vortices interpreted as particles; their circulation encodes spin and generates Bernoulli pressure gradients seeded near the core by the associated quantum potential, which upon many-vortex coarse-graining yield macroscopic gravitational acceleration. Painlevé-Gullstrand river coordinates geometrically encode thismaterial dynamics in general-relativistic exterior solutions, recovering classical weak- and strong-field benchmarks, including leading Kerr-Lense-Thirring behavior. At galactic scales, an isothermal regime of \(\phi\) yields nearly flat rotation profiles, thereby providing a quantum-hydrodynamic route to MOND-like phenomenology. Cosmologically, expansion is treated as a coarse-grained deformation of the DDF, with primordial vortex-antivortex annihilation as a possible trigger for the hot epoch and inflation-like expansion, while the cosmic web is associated with vortex-filament networks in doped superfluids. Together, these results define a unified dark-medium framework; the Appendices present a direct gravitational discriminator from general relativity, an astrophysical probe of the proposed superfluid interpretation of the cosmic web, and laboratory tests of the DDF constitutive rheology.