Distinct acceleration relations of galaxies and galaxy clusters from hyperconical modified gravity

General relativity (GR) is the most successful theory of gravity, with great observational support on local scales. However, to keep GR valid over cosmic scales, some phenomena require the assumption of exotic dark matter, especially the cosmic expansion history and flat rotation curves of galaxies. Their radial acceleration relation (RAR) indicates a tight correlation between the dynamical mass and the baryonic mass. This suggests that galactic observations could be better explained by modified gravity theories without exotic matter. Modified Newtonian dynamics (MOND) is an alternative theory that was originally designed to do exactly this using a new fundamental acceleration scale, a₀, the so-called Milgromian parameter. However, this nonrelativistic model lacks the flexibility needed to account for the wide variety of observed phenomena. In contrast, a relativistic MOND-like gravity naturally emerges from the hyperconical model, which derives a fictitious acceleration compatible with observations. We analyze the compatibility of the hyperconical model with respect to distinct RAR observations of 10 galaxy clusters obtained from HIFLUGCS and 60 high-quality SPARC galaxy rotation curves. The results show that a general relation can be fitted to most cases with only one or two parameters, with an acceptable χ² and p-value. These findings suggest a possible way to complete the proposed modification of GR on cosmic scales.