Fractional Field Theory and Physics of the Dark Sector

Abstract

Derived from the Peccei-Quinn (PQ) mechanism, axions are hypothetical pseudo-Goldstone bosons that restore the charge-parity (CP) symmetry of quantum chromodynamics (QCD). As of today, the mainstream view is that the PQ mechanism offers the most plausible explanation on the puzzle of preserving CP symmetry in QCD. Moreover, several astrophysical models postulate that axions are likely components of Cold Dark Matter (DM). For example, a recent study argues that DM behaves as a strongly coupled superfluid phase consisting of axion-like particles with mass in the eV range or below [1]. Despite these attractive features, experimental searches have either ruled out some axion-based models or placed them under stringent exclusion limits. The object of this work is to show that the concept of spacetime equipped with minimal fractality (the so called minimal fractal manifold, MFM in short [2-5]) solves the CP problem of QCD without invoking the PQ paradigm. Rather than discarding axions as superfluous complications of the theory, we conclude that they may be seen as topological signature of the MFM, which we suggestively refer to as “Cantor Dust”. We tentatively find that the properties of “Cantor Dust” match current observations of DM on both cosmological and galactic scales. They also fall in line with the idea that Dark Energy arises from the dynamics of neutrino oscillations on cosmological scales [6].