Modified Gravity from Nonlinear Structural Persistence: A Covariant Scalar–Tensor Alternative to Dark MatterFramework with Empirical Closure Across Dynamics and Lensing (V.6-2025-09-01)

This work introduces a covariant scalar–tensor theory of gravity in which galactic-scale gravitational phenomena arise from the dynamics of a scalar field � representing structural persistence of baryonic matter distributions. The theory modifies General Relativity through a nonlinear kinetic sector that produces MOND-like dynamics in low-acceleration environments while recovering standard General Relativity in high-density regimes through a screening mechanism. The framework is constructed from a well-defined relativistic action in which the scalar field couples to matter through a saturating conformal transformation of the metric. The nonlinear kinetic function generates a transition between three gravitational regimes: a Newtonian/General Relativistic regime at high acceleration, a transition regime where scalar effects become significant, and a deep modified-gravity regime that reproduces the observed baryonic Tully–Fisher relation. In the weak-field limit the theory predicts a modified acceleration law in which the scalar contribution dominates in galactic outskirts, naturally producing flat galaxy rotation curves without invoking non-baryonic dark matter. The model also incorporates a scalar potential that introduces Yukawa suppression in dense environments, ensuring compatibility with Solar System tests of gravity. Beyond galactic dynamics, the theory provides predictions for gravitational lensing, structure formation, and cosmological perturbations. The scalar field contributes an effective stress–energy component that modifies the growth of cosmic structure through a scale-dependent effective gravitational coupling while preserving the standard cosmological expansion history during early epochs. Stability conditions for the scalar sector are analyzed, demonstrating that the theory remains free of ghost and gradient instabilities within the physical parameter regime. The resulting framework provides a unified description of galaxy rotation curves, gravitational lensing, and cosmological structure growth within a single covariant modified-gravity theory. An observational program is outlined to test the theory through galaxy rotation curves, weak lensing measurements, and cosmological growth-rate observations.