Vacuum–Spacetime Coupling as an Origin of Galactic Rotation Curves

We present a framework in which dark matter phenomenology arises from a nonlinear coupling between vacuum energy (dark energy) and spacetime curvature. Gravity itself remains unmodified; instead, vacuum energy contributes an effective gravitational source only in weak-field regimes. A curvature-dependent vacuum coupling leads to a nonlinear Poisson equation whose weak-field asymptotic solution naturally produces flat galactic rotation curves and the baryonic Tully–Fisher relation, where the acceleration scale emerges directly from the cosmologicalc onstant. No dark matter particles, no modification of inertia, and no additional free parameters are introduced.