Gravity with a Dynamically Generated Yukawa-Type Potential: A Unified Description of Galactic Rotation Curves and Cluster Lensing

We present a framework for gravity in which the effective interaction is described by a dynamically generated Yukawa-type potential arising from nonlinear field self-interactions. In this approach, the characteristic scale is not imposed but emerges directly from the field equations, leading to a scale-dependent gravitational interaction. The resulting potential is intrinsically non-perturbative and reduces to standard General Relativity in high-density regimes. We show that this framework naturally reproduces flat galaxy rotation curves and the Tully–Fisher relation, while also providing enhanced gravitational lensing consistent with cluster observations. Using representative fits to dwarf and spiral galaxies, as well as cluster convergence profiles, we demonstrate that a single dynamical mechanism can account for both kinematic and lensing phenomena without invoking dark matter or empirical acceleration scales. These results suggest that gravity may be fundamentally a self-interacting field with an emergent, environment-dependent range.