A Suggested Alternative to Dark Matter in Galaxies: I. Theoretical Considerations

Dark matter is the generally accepted paradigm in astrophysics and cosmology as a solution to the higher rate of rotation in galaxies, among many other reasons. But since there are still some problems encountered by the standard dark matter paradigm at the galactic scale, we have resorted to an alternative solution, similar to Milgrom's Modified Newtonian dynamics (MOND). Here, we have assumed that: (i) either the gravitational constant, G, is a function of distance (scale): G = G(r), or, (ii) the gravitational-to-inertial mass ratio, mg/mi, is a function of distance (scale): f(r). We have used a linear approximation of each function, from which two new parameters appeared that have to be determined: G1, the first-order coefficient of gravitational coupling, and C1, the first-order coefficient of gravitational-to-inertial mass ratio. In the current part of this research, we have generated simplified theoretical rotation curves for some hypothetical galaxies by varying the parameters. We have concluded that our model gives a qualitatively and quantitatively acceptable behavior of the galactic rotation curves for some values of these parameters. The values of the 1st-order coefficients that give quantitatively acceptable description of galactic rotation curves are: G1 between around 10^-31 to 10^-30 m^2 s^-2 kg^-1; and, C1 between 10^-21 to 10^-20 m^-1. Furthermore, our model implies the existence of a critical distance at which the MOND effects become significant rather than a critical acceleration. In fact, Milgrom's MOND converges with our model if the critical acceleration is not a constant but a linear function of the galactic baryonic mass.