From Axion—Neutrino Couplings to Axion Thermodynamics: Testing the Axion Mass Hierarchy

The composition and physical state of dark matter remain among the most pressing unresolved questions in modern physics. Addressing these questions is crucial to our understanding of the Universe’s structure. In this work, we explore the hypothesis that massive scalar bosons, such as axions, constitute the majority of dark matter. We focus on two key aspects of axion physics: (i) the role of axion–neutrino coupling in generating neutrino mass and (ii) the thermodynamic properties of axion dark matter. We propose that the interaction between neutrinos and axions in the early Universe, prior to hadronic formation, could provide a mechanism for finite neutrino masses. Furthermore, to account for the observed large-scale distribution of dark matter, we extend the Bose–Einstein condensation framework and derive the critical temperature T$_c$ that defines the onset of the condensate phase. Our calculations suggest that this temperature ranges from a few 10$^{−3}$ degrees Kelvin to approximately one Kelvin, depending on the axion scale factor f$_a$. These findings support the plausibility of axions as viable dark matter candidates and emphasize the importance of future experimental searches for axion–neutrino interactions. Additional astrophysical and laboratory investigations could further refine axion mass constraints and shed light on the role of axion condensates in the evolution of the early Universe.