Inverse Mass Law for Dark Matter: A Novel Geometric Alternative to Particle Candidates

This work introduces a new theoretical framework called the Inverse Mass Law, which provides a geometric and energy-density-based explanation for dark matter effects without requiring unknown particle candidates. The model proposes that the apparent gravitational mass of astrophysical systems arises from variations in vacuum energy density and space-time curvature. A reciprocal relationship between effective mass and vacuum energy is formulated, offering a unified interpretation of galactic rotation curves, gravitational lensing, and mass anomalies. The paper develops the mathematical foundations of the theory, including the core equation m_eff = k / ρ_v, where mass is treated as an emergent quantity influenced by vacuum energy distribution. The framework extends to cosmological scales, connecting the observed expansion rate and dark energy density with the geometric structure of space. Predictions, testable consequences, and potential links to quantum gravity are discussed. This preprint aims to provide an alternative viewpoint on dark matter by treating mass not as an intrinsic property of particles, but as a geometric response of space-time to underlying vacuum fluctuations.