A Six-Force Framework: Compatibility of Axial Dark Interactions and Chameleon Cosmology as Solutions to Three Contemporary Anomalies

This work presents a phenomenological extension of the Standard Model and general relativity in which two additional interactions are introduced alongside the four known fundamental forces. The resulting Six-Force Framework incorporates an axial dark interaction and a chameleon scalar force to address three persistent anomalies in contemporary physics: the muon anomalous magnetic moment, small-scale structure discrepancies associated with dark matter, and the observed acceleration of cosmic expansion. The axial dark interaction is realized through a light mediator with predominantly axial couplings to muons and dark matter. This interaction simultaneously generates loop-level contributions to the muon anomaly and velocity-dependent dark matter self-interactions consistent with astrophysical observations across dwarf galaxies and galaxy clusters, while remaining compatible with collider, direct detection, and cosmological constraints. The chameleon scalar force provides a dynamical explanation for dark energy via a density-dependent screening mechanism. This mechanism suppresses fifth-force effects in high-density environments while allowing the scalar field to drive late-time cosmic acceleration in low-density regions, thereby maintaining consistency with laboratory, Solar System, and cosmological tests of gravity. A central organizing principle of the framework is the pairing of interactions across physical regimes: strong–weak at nuclear scales, electromagnetic–axial dark at particle and galactic scales, and gravity–chameleon at cosmological scales. While not derived from a fundamental symmetry, this pairing offers a structured phenomenological perspective that unifies disparate extensions of known physics without invoking a single overarching theory. The framework is modular, testable, and falsifiable, and it makes concrete predictions for particle physics experiments, astrophysical observations, and precision tests of gravity. This work is intended as a compatibility and synthesis study rather than a claim of theoretical completeness, providing a foundation for further theoretical development and experimental investigation.