Abstract
This work introduces a finite-range modification of gravity, in contrast to the infinite range assumed in Newtonian theory and General Relativity. When a mass is embedded in a vacuum with nonzero energy density, it generates a confined gravitational field, bounded by a specific radius beyond which gravity vanishes and dark energy governs cosmic dynamics.
Gravitational interactions are quantified by a scaling factor that measures the degree of overlap between field volumes: overlap yields attraction, touching boundaries produce zero force, and separation eliminates gravity entirely, leaving cosmic expansion as the dominant effect. Incorporating this factor modifies Newtonian gravity and General Relativity, providing an accurate representation of gravitational forces on cosmological scales while preserving local tests.
The framework offers a predictive mechanism and natural explanation for the binding of galaxies within clusters and the recession of distant systems. Moreover, it provides a resolution to the S₈ tension, one of cosmology’s most persistent anomalies, without invoking exotic dark-sector physics.