An empirical analysis of the dynamics of both individual galaxies and gravitational lensing in galaxy clusters without dark matter

Abstract: The existence of the flat rotation curves of galaxies is still perplexing. The dark matter paradigm was proposed long ago to solve this conundrum; however, this proposal is still under debate. In this paper, we search for universal relationships solely involving the baryonic density that incorporate both galactic dynamics and gravitational lensing in galaxy clusters without requiring dark matter. If this type of formula exists, we show that it is possible that it can clearly indicate that dark matter is either perfectly tailored to baryonic matter or, from a more radical point of view, even perhaps useless. If the latter situation is true, then we must give greater visibility to models such as modified inertia (MOND) or even modified gravity (MOG).