Newtonian Fractional-Dimension Gravity and Dark Matter

We summarize the main results of Newtonian Fractional-Dimension Gravity (NFDG), an extension of the standard laws of Newtonian gravity to lower dimensional spaces, including those with fractional (i.e., non-integer) dimension. We apply our model to several rotationally supported galaxies (NGC 7814, NGC 6503, NGC 3741, NGC 5033, NGC 6674, NGC 5055, and NGC 1090) and to some notable cases of galaxies with little or no dark matter (AGC 114905 and NGC 1052-DF2). We also consider the case of the Bullet Cluster merger (1E0657-56), assumed to be one of the strongest proofs of dark matter existence.

In all these cases, NFDG is able to fit the rotation curves of these galaxies and also explain the dynamics of the Bullet Cluster merger without employing any dark matter components. This is done by using a fractional-dimension function D(R), which characterizes each individual galaxy, together with the equations of Newtonian gravity extended to spatial dimension D < 3. Possible connections between NFDG and Modified Newtonian Dynamics (MOND) are analyzed and a relativistic version of NFDG is also introduced.