A Falsifiable Effective Framework for Superfluid Vacuum Dynamics in Cosmology and Galaxies

This paper proposes a theoretical cosmology framework where classical spacetime is reinterpreted as an emergent superfluid vacuum described by a Bose-Einstein condensate under a nonlinear logarithmic Schrodinger equation (LogSE). We present a two-phase model: the homogeneous ground state (Phase A) accounts for cosmic acceleration (dark energy) and resolves the Hubble tension via bulk viscosity, while excited states (Phase B) manifest as quantized vortices and solitons acting as dark matter halos. The framework naturally yields a cosmic equation of state w ≈ -1 and MOND-like galactic phenomenology without requiring new particle species. Furthermore, we demonstrate that quantum pressure from the LogSE resolves the core-cusp problem by stabilizing galactic cores. The model is confronted with constraints from precision multimessenger timing (GW170817) and ultra-high-energy gamma-ray observations (LHAASO) regarding emergent Lorentz invariance.