Emergent Spacetime and Parametric Time: A Unified Superfluid Vacuum Framework for Cosmology and Galactic Dynamics

The incompatibility between the dynamical time of General Relativity and the absolute time parameter of Quantum Mechanics constitutes the ”Problem of Time,” a fundamental hurdle in quantum gravity. This paper proposes a resolution by positing that time is fundamentally a non-dynamical calculation parameter governing the evolution of a quantum superfluid vacuum, from which classical spacetime geometry emerges. We construct a unified cosmological framework based on the Logarithmic Schrödinger Equation (LogSE), identifying the vacuum’s ground state with Dark Energy and its excited states with Dark Matter. We demonstrate that the emergent bulk viscosity of the vacuum ground state naturally resolves the Hubble Tension by inducing a late-time phantom-like equation of state. Furthermore, the model eliminates the Big Bang singularity via a Janus Point phase transition and resolves the galactic Core-Cusp problem through quantum pressure stabilization. The framework is consistent with current constraints on Lorentz Invariance Violation (LHAASO, GW170817) while offering falsifiable predictions for ultra-high-energy dispersion relations.