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 foundation for a unified reading of Lorentz-symmetric operational kinematics, gravitational dynamics, and cosmological phenomenology. The proposed substrate is a two-component CDM medium in which an ultralight superfluid scalar sector (\ (\) ) acts as the continuous phase of the DDF and a sector (\ (\) ) of heavier bosons constitutes the dispersed jamming phase. The presence of a dispersed phase yielding a dilatant response under stress is the crucial element that distinguishes this proposal from earlier superfluid-vacuum approaches, as well as from emergent-spacetime paradigms. Three domains are developed from the hydrodynamics of the DDF: the electromagnetic sector and SR-like operational kinematics, gravity, and cosmological phenomenology. Relativistic kinetic energy, length contraction, time dilation, and interferometric null results are interpreted as material effects due to the dilatant response produced by the DDF when it is stressed by the motion of massive bodies. In this reading, the Lorentz factor is recovered as the effective jamming factor of the DDF, while ordinary and orbital motions remain in a negligible-drag regime because the jamming factor grows slowly at low velocities and acceleration scales inversely with the mass of the body, becoming especially suppressed for large celestial bodies. The superfluid sector is proposed to provide a hydrodynamic account of gravitational phenomenology: fundamental massive particles are modeled as quantized vortices of \ (\), with spin arising from circulation and gravity from the associated Bernoulli pressure deficit. Einstein solutions are therefore read in Painlevé–Gullstrand variables as effective quantum-hydrodynamic configurations, allowing weak-field tests and strong-field phenomenology to be reframed as DDF responses, while MOND-like galaxy behavior is attributed to isothermality of the dark superfluid in galactic outer regions. From a cosmological perspective, large-scale structure is modeled as vortex–filament morphology of the coupled medium, by analogy with rotating doped superfluids; BAO-like correlations are associated with the mean vortex spacing; and cosmological redshift is attributed primarily to weak material expansion of a rotating DDF-bubble Universe, generated by centrifugal outflow and partly opposed by Bernoulli forcing and vortex-filament structure. The CMB is identified with the thermal \ (\) -radiation bath projected through the DDF expansion, while CMB/BAO transfer calculations, complete cosmological likelihood analyses, and a full Standard-Model embedding of the vortex-particle domain are left for subsequent work. Empirical discriminants are developed in the Appendices, making the theory a falsifiable dark-substrate proposal.