A Unified Framework for Speed‑Dependent Gravity, Dark Matter Dynamics, and Cosmic Structure Formation (Version 2)

Description / Abstract This Version 2 release expands the original speed‑dependent gravity framework into a complete theoretical model grounded in variational principles, covariant field theory, and dynamical stability analysis. The central postulate remains that a particle’s gravitational influence scales with its velocity via an effective coupling Geff=G(1+αv2/c2), generating a self‑reinforcing feedback loop between speed, acceleration, and gravitational strength. Version 2 adds four major theoretical components: (1) a Newtonian‑limit Lagrangian that reproduces the velocity‑dependent force law; (2) a covariant relativistic extension in which the velocity dependence arises from modifications to the effective stress‑energy tensor of a dark sector field; (3) a full linear and nonlinear stability analysis demonstrating that the feedback loop is self‑limiting and cosmologically stable; and (4) observational and theoretical constraints on the coupling parameter α. These additions resolve the primary critiques of the original model and establish a complete, self‑consistent, and testable physical theory capable of explaining cosmic filaments, voids, and ultra‑fast dark matter without requiring cold dark matter initial conditions.