Tensorial vacuum condensate: Emergent dark matter phenomenology from an effective field theory

The physical origin of the ``missing mass'' driving galactic kinematics and cosmic structure formation remains one of the most profound open questions in modern astrophysics. Here, we propose the Tensorial Dynamical Vacuum (TDV) framework, a Lorentz-covariant effective field theory (EFT) that conceptualizes the spacetime vacuum as a macroscopic quantum condensate. We demonstrate that the macroscopic geometric relaxation of this condensate around the critical cosmic acceleration scale (a₀ c H₀) naturally recovers the empirical Baryonic Tully-Fisher relation and provides a geometric mechanism for flat galactic rotation curves. Furthermore, the framework suggests that the non-linear dynamics of galaxy cluster mergers, such as the Bullet Cluster, might be understood through a finite geometric response time governed by the effective sound speed of the vacuum (cₛ c). This retardation induces an effective dynamical inertia, allowing the global gravitational potential to transiently decouple from rapidly decelerated baryonic gas. Consequently, the framework offers a natural mechanism to replicate key phenomenological signatures traditionally attributed to collisionless dark matter halos, providing a complementary geometric perspective to standard particulate paradigms. Crucially, the model is constructed to maintain consistency with high-precision Solar System and multi-messenger tests through a universal effective metric and an intrinsic dynamical screening mechanism. In the extreme strong-field regime proximate to compact objects, the theory points toward a unique topological signature of macroscopic linear gravitational birefringence, strictly bounded below current polarimetry detection thresholds to rigorously preserve standard Einsteinian gravity. By formulating the macroscopic vacuum response tensor _ as the fundamental dynamical degree of freedom, the theory minimizes empirical parameters and proposes a purely geometric perspective on emergent dark matter phenomenology.