Relativistic quantum corrections to classical dynamics as an alternative to dark matter and dark energy

Classical physics and visible matter are insufficient to account for cosmic phenomena such as flat galactic rotation curves or the apparent acceleration of the universe, leading to the conventional introduction of dark matter and dark energy. However, their persistent invisibility suggests that these effects may stem not from hidden components but from deeper physical principles. Here we propose that the dark-sector phenomenology emerges from nonlinear quantum forces absent in classical dynamics, originating from the infinite hierarchy of quantum corrections in the Wigner-Moyal phase-space formulation. Previous studies have shown that these higher-order corrections vanish under coarse resolution yet grow exponentially when the system is resolved more finely. We reinterpret this resolution-dependent quantum complexity as a relativistic effect amplified by gravitational potential, whose normalization reproduces spacetime curvature in the weak-field limit and generates additional forces on cosmic scales. When the mass distribution can be described as a macroscopic wave packet, the resulting quantum corrected force naturally reproduces galactic rotation curves without invoking dark matter. Conversely, when the background potential defining the quantum corrections is tied to the observer’s causal horizon, it weakens with distance, causing the quantum terms to diminish and the dynamics to gradually converge toward classical behavior—making the faraway universe appear to contain less dark matter. This horizon-dependent suppression naturally reduces the inferred luminosity distances of distant galaxies, accounting for the Pantheon+ Type Ia supernova data without invoking dark energy and giving the impression of an accelerating universe. Our results suggest that the combined phenomenology of relativity, dark matter, and dark energy may arise from gravitationally regulated quantum statistical dynamics, offering a unified and observationally consistent alternative to the standard dark-sector paradigm.