Another New Modified Gravity Theory

There are many variations on the modified gravity theory MOND that solve or mostly solve the dark matter problem without dark matter. The latest one solves this in the case of both galaxies and 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 is MOdified Newtonian Dynamics (MOND). MOND was first published by Mordehai Milgromin 1983. 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 not been 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 κ-model, based on very elementary phenomenological considerations, has recently been proposed in the astrophysics field. This model shows that the presence of dark matter can be considerably minimized with regard to the dynamics of galaxies (Pascoli, 2022 a,b). The κ-model belongs to the general family of theories descended from MOND. Under this family of theories, there is no need to develop a highly uncertain dark matter sector of physics to explain the observations.

Gianni Pascoli, "A comparative study of MOND and MOG theories versus the κ-model: An application to galaxy clusters" arXiv:2307.01555 (July 4, 2023).

The 2022a paper that expounds the theory has the following abstract:

The determination of the velocities, accelerations and the gravitational field intensity at a given location in a galaxy could potentially be achieved in an unexpected manner with the environment of the observer, for instance, the local mean mass density in the galaxy. 

This idea, mathematically supported by the asymmetric distance concept, is illustrated here by a study regarding the rotation of spiral galaxies. This suggestion is new in the astrophysics field (in the following, it is called the kappa-model) and could help to mimic the main effects seen in modified Newtonian dynamics (MOND) theory, modified gravity (MOG) models, or other related models built with the aim of eliminating dark matter that are already well-established theories. 

Thus, starting from two selected examples of galaxies, in section 5, we show that there is an equivalence between MOND and the kappa-model. In particular, on the opposite side, we have the speculative nature of the dominant paradigm, the elusive dark matter, a matter whose properties always remain undefined despite intense theoretical, experimental and observational efforts for over 50 years.

Neither article does a good job of succinctly summarizing how the model works.