A comparative study of MOND and MOG theories versus the$\kappa$-model: An application to galaxy clusters

Many models have been proposed to minimize the dark matter (DM) content in various astronomical objects at every scale in the Universe. The most widely known model isMOdified Newtonian Dynamics (MOND). MOND was first published by Mordehai Milgromin 1983 (Milgrom, 1983; 2015; see also Banik and Zhao, 2022 for a review). A second concurrent model is modified gravity (MOG), which is a covariant scalar-tensor-vector (STVG)extension of general relativity (Moffat, 2006; 2020). Other theories also exist but have notbeen broadly applied to a large list of astronomical objects (Mannheim and Kazanas, 1989;Capozziello and De Laurentis, 2012; O'Brien and Moss, 2015; Verlinde, 2017). A new model,called $\kappa$-model, based on very elementary phenomenological considerations, has recently beenproposed in the astrophysics field. This model shows that the presence of dark matter canbe considerably minimized with regard to the dynamics of galaxies (Pascoli, 2022 a,b). The$\kappa$-model belongs to the general family of theories descended from MOND. Under this familyof theories, there is no need to develop a highly uncertain dark matter sector of physics toexplain the observations