The Vijay Flux–Shadow Gravity Model: A Unified Alternative to Dark Matter

This work proposes the Vijay Flux–Shadow Gravity Model, a novel gravitational framework that replaces the need for particle dark matter while retaining dark energy as the underlying driver of cosmic expansion. The model is built on two physical ingredients: (1) a cosmic flux term generated by large-scale vacuum expansion associated with dark energy, and (2) a baryon-linked shadow term that modifies local gravitational potentials through geometric flux obstruction rather than non-baryonic matter.

The formulation satisfies all essential consistency conditions, including the Poisson equation, Friedmann equations, Raychaudhuri equation, Jeans stability, stress-energy conservation, and Maxwell-type constraints. It recovers Newtonian gravity in spherical systems, produces flat galactic rotation curves, and reproduces key features of weak lensing and cluster dynamics. The resulting effective mass profile naturally generates logarithmic mass growth without invoking particle dark matter.

The framework integrates smoothly into relativistic cosmology, offering a geometric mechanism for structure formation and gravitational enhancement while preserving the standard role of dark energy. This deposition presents the complete formulation of the model—including action construction, field equations, covariant shadow dynamics, and observational consequences—and invites the scientific community to perform independent numerical tests, such as CMB power-spectrum evaluations and Boltzmann-code simulations.