On the physical origin of the radial acceleration relation

Abstract

The radial acceleration relation (RAR) is a tight correlation between the distribution of baryonic matter in galaxies and their observed dynamics, even in systems where dark matter dominates. This suggests a universal acceleration scale exists in galaxies, which appears to challenge the $Λ$CDM standard cosmological model and favor Modified Newtonian dynamics (MOND). However, MOND also deviates from the RAR, so these deviations are not fully explained by the $Λ$CDM model or MOND. A theory that explains gravity and the dark sector geometrically, and treats dark matter as a spin-1 particle, is required, such as Modified General Relativity (MGR). It is the only metric-compatible theory of gravity that describes local gravitational energy-momentum by the connection-independent symmetric tensor $\varPhi_{αβ}$, which completes the total energy-momentum tensor of the Einstein equation. Dark energy is explained by the energy-related component $\varPhi_{00}$, and dark matter by the stress components $\varPhi_{ij}$. Dark matter is extremely difficult to observe because it is fundamentally related to the Lorentzian metric of spacetime itself. The physical origin of the RAR follows directly from the equilibrium between the dark energy and Newtonian forces in the outer part of the rotation curve of galaxies or galaxy clusters, and that between the dark sector forces in the inner part of the rotation curve. It is shown that MGR subsumes MOND, accounts for the gravitational anomaly observed in wide binaries, and exhibits the observed Newtonian behavior of gravity at large scales.