Entropy of Cantor Dust and Fuzzy Dark Matter

Abstract

Fuzzy Dark Matter (FDM) models are of class of theories where Dark Matter (DM) is interpreted as condensate of ultralight scalar or pseudo-scalar particles. Few years back we conjectured that a spacetime endowed with minimal fractality enables a natural association of FDM to Cantor Dust, an early Universe phase induced by topological condensation of continuous dimensions. Appealing to the maximal entropy of Cantor Dust, this brief note recovers the mass of FDM particles in reasonable agreement with simulations and cosmological data. An intriguing finding is that, at least in principle, the entropy of Cantor Dust can also account for the non-vanishing photon mass in Proca-Stueckelberg models.