The expansion of the universe could be a mirage, new theoretical study suggests

Perhaps the model contains some valuable idea, but its conclusions are presented in a certainly wrong way, because in order to claim that the masses are varying in time it is first necessary to give a definition of a system of fundamental units of physical quantities where this is true.

For instance, if the mass of the electron is the unit of mass, then no masses can vary in time, even in this model.

In a correct formulation of this model, what could vary in time would be either the Newtonian constant of gravitation alone or some combination between the Newtonian constant of gravitation and other quantities that are considered fundamental constants, like the strength of the electromagnetic interaction (which is usually named "fine structure constant") or the Planck constant or the speed of light.

It may be useful to try to understand the paper by reformulating its equations in a rigorous way, compatible with the SI system of units. It should be noted that time is currently measured based on differences between atomic energy levels, which depend on the masses of the elementary particles. Therefore it is impossible to formulate correctly a physical model where the masses vary in time before giving other definitions for time and mass, to remove the dependency between the units of these quantities.

In conclusion, because this model is formulated starting from equations devoid of physical meaning (because it is not specified what physical quantities are the so-called "mass" and "time" in those equations), I believe that it is more likely that the results are garbage instead of being useful, though the paper may still merit to be studied.