An interesting equation yields the MOND but does not rule out the dark matter

Abstract: Inspired by the idea in Ref. [16], which introduced a viscosity coefficient into the expansion equation describing the universe, we also attempt to introduce such a positive viscosity coefficient into the rotational motion equation describing the galaxies, and then studies what will happen. Surprisingly, we obtained all the formulas assumed in MOND, including a concrete interpolation function between the centripetal acceleration and the Newtonian acceleration. But at the same time, something different from MOND was also obtained, that is, the critical acceleration, a0 in MOND, does not need to be a constant, but increases with the mass of the galaxy increases, and under the action of viscosity coefficient, the rotational galaxies will gradually expand over time at the radial direction, just like the expansion of the universe. However, unlike MOND, the model in this paper cannot rule out the existence of dark matter. Instead, the mass of dark matter can be used to help to adjust the value of A0 (here it just to distinguish from a0 in MOND, and A0 and a0 have the same meaning in the equation), thereby helping to better fit the radial acceleration relation (RAR) curve of galaxies. However, unlike ΛCDM, even if dark matter exists, it does not need to be carefully adjusted to meet the asymptotically flat rotational velocity curve of galaxies. The rotational curve of galaxies with this characteristic can be also achieved under the viscous dynamics of the galaxy itself.