Quantum Hydrodynamic Gravity: Replacing the Cosmological Constant with Superfluid Quantum Pressure and Resolving Gravitational Singularities

Modern theoretical physics remains divided between the deterministic geometricframework of General Relativity and the probabilistic structure of quantum mechanics. While Einstein’s field equations accurately describe gravitational phenomena across astrophysical scales, they exhibit two profound theoretical shortcomings:the prediction of curvature singularities and the introduction of the unexplainedcosmological constant. This research proposes a unified quantum-hydrodynamicframework in which the cosmic vacuum is modeled as a quantum superfluid governed by the Madelung transformation of the wavefunction. By embedding thequantum potential into a modified hydrodynamic form of the Navier–Stokes equations, I derive a self-consistent quantum pressure term capable of both regularizinggravitational collapse and dynamically generating cosmic acceleration. I demonstrate that the quantum potential introduces an intrinsic repulsive force proportional to density curvature. At cosmological scales, the average quantum potentialsatisfies an emulation condition that reproduces the equation-of-state parameterw ≈ −1, effectively replacing the cosmological constant with emergent superfluiddynamics. Furthermore, the Fisher information energy associated with densitygradients generates an asymptotic energy barrier that prevents the formation ofgravitational singularities, replacing them with stable quantum cores. This framework provides a deterministic interpretation of cosmic evolution in which darkenergy emerges naturally from the dynamics of a quantum fluid vacuum