Minimal Fractal Manifold & the Dual Nature of Dark Matter

Abstract

As of today, the nature of Dark Matter (DM) remains controversial. Broadly speaking, there are two major schools of thought on the topic. While the first school considers DM to be an extrapolation of particle physics, the second one asserts that DM is a signature of gravitational phenomena. The basic tenet of the second school of thought is that DM can be explained away either through revisions of General Relativity (GR), through its inherent nonlinearity or by deploying non-traditional interpretations of GR. The goal of this brief note is to point out that DM and gravitational physics may no longer be mutually exclusive, but complementary manifestations of the same reality. Elaborating from the minimal fractality of spacetime above the Fermi scale - along with its quaternion formulation - we suggest that DM can replicate the contribution of gravitational nonlinearities on galactic scales.