Dilatant Dark Fluid: Toward a Quantum-Hydrodynamic Dark-Substrate Framework for Relativistic and Cosmological Phenomenology

This work introduces a cosmic dilatant (shear-thickening) dark fluid (DDF) as a candidate quantum-hydrodynamic dark substrate for operational relativistic kinematics, gravity, and cosmological phenomenology. The DDF is a two-component cold-dark-matter medium comprising an ultralight superfluid scalar sector \(φ\), which forms the continuous phase, and a heavier bosonic sector \(φ\), which forms a dispersed jamming phase. The stress-induced dilatancy of this dispersed component distinguishes the model from earlier superfluid-vacuum approaches. Electromagnetic propagation and special-relativistic operational effects are attributed to the response of the \(φ\) sector. Relativistic kinetic energy, length contraction, time dilation, and interferometric null results arise from reversible speed-dependent jamming, with the Lorentz factor recovered as the effective jamming factor: during acceleration, the additional energy required by the dilatant response of the medium is the same energy normally described as relativistic kinetic energy. This response does not introduce an additional macroscopic drag or secular orbital slowdown, and the low-speed limit reproduces Newtonian and post-Newtonian behavior. Gravity is modeled as the Bernoulli response of the superfluid \(φ\) sector to quantized vortex/defect matter, with particle spin associated with circulation. Standard Einstein solutions are represented in Painlev\'e--Gullstrand variables as effective hydrodynamic configurations. At galactic scales, localized bound or entrained \(φ\)-halo loading contributes to the active source, lensing mass, and circular-velocity amplitude, while isothermality of the \(φ\) sector in the low-acceleration regime is the primary mechanism producing the approximately flat outer radial profile. Large-scale structure is interpreted as a vortex--filament morphology of the coupled medium, by analogy with laboratory doped superfluids, with baryon-acoustic-oscillation (BAO)-like correlations associated with the mean spacing of filament bundles. Cosmological redshift is attributed primarily to weak material expansion of a rotating DDF-bubble Universe, driven by centrifugal outflow and opposed in part by Bernoulli forcing and filament structure. The cosmic microwave background (CMB) is treated, at framework level, as the thermal \(φ\)-radiation bath observed through this expansion. Full CMB/BAO transfer calculations, cosmological likelihood analyses, and a Standard-Model embedding remain for future work. The proposed observational discriminants make DDF a falsifiable dark-substrate framework.