Emergent dark matter phenomenology from a tensorial dielectric vacuum

The physical nature of dark matter remains one of the most pressing questions in astrophysics. Here, we propose the Tensorial Dielectric Vacuum (TDV) framework, an effective field theory that models the vacuum as a polarizable macroscopic condensate. We demonstrate that vacuum dielectric saturation at the cosmic acceleration scale (a₀ cH₀) recovers the Baryonic Tully-Fisher relation and naturally accounts for galactic rotation curve anomalies. Furthermore, the framework addresses the dynamics of galaxy cluster mergers, such as the Bullet Cluster, by introducing a vacuum relaxation mechanism. The finite response time of the vacuum induces a dynamical inertia, allowing the gravitational potential to transiently decouple from decelerating baryonic matter. This ``dielectric memory" effect mimics the behavior of collisionless dark matter without invoking non-baryonic particle species. The TDV model remains consistent with Solar System precision tests through an intrinsic screening mechanism. In the strong-field regime, it provides falsifiable predictions for future X-ray polarimetry missions, notably a unique signature of gravitational birefringence distinct from quantum electrodynamic (QED) effects. By formulating the vacuum polarization tensor _ as the fundamental dynamical degree of freedom, the theory preserves global Lorentz covariance and avoids ad-hoc background structures, offering a rigorous, purely tensorial mechanism for emergent dark matter phenomenology.