The Tensorial Dielectric Vacuum: Emergent Dark Matter Phenomenology from a Superfluid Condensate

Based on the Effective Field Theory limit of a Lorentz-covariant ground state, we propose the Tensorial Dielectric Vacuum (TDV) framework. Unlike standard General Relativity which interprets gravity purely as geometry, TDV models the vacuum as a polarizable superfluid condensate. We demonstrate that the breakdown of linear coherence at the cosmic acceleration scale (a₀ cH₀) naturally resolves the galactic rotation curve anomaly via a dielectric saturation mechanism, recovering the Baryonic Tully-Fisher relation. Crucially, we address the challenge of galaxy cluster mergers (e. g. , the Bullet Cluster) by introducing a vacuum relaxation mechanism. We show that the vacuum's finite response time induces a dynamical inertia, allowing the gravitational potential to transiently decouple from decelerating baryonic matter. This ``dielectric memory" effect mimics collisionless dark matter without invoking exotic particle species. In the strong-field regime, the theory predicts a unique signature of gravitational birefringence, a polarization-dependent Shapiro delay distinct from QED effects. This framework remains consistent with Solar System constraints via a screening mechanism while providing falsifiable predictions for future X-ray polarimetry missions like eXTP. Crucially, the theory is formulated with the vacuum polarization tensor _ as the fundamental dynamical degree of freedom; the vector field u^ emerges geometrically as its timelike eigenvector, ensuring Lorentz covariance and eliminating ad-hoc background structures.