"Invisible" QCD axion rolling through the QCD phase transition

TL;DR

This paper investigates the QCD phase transition in the early universe and estimates the current energy density of cold dark matter composed of invisible QCD axions, based on the dynamics of the phase change.

Contribution

It provides a detailed analysis of the QCD phase transition's timing, supercooling effects, and their implications for the present-day abundance of invisible QCD axion dark matter.

Findings

Effective bubble formation rate $eta(T) \\approx 10^{4-5}$ MeV.

Completion temperature of phase transition $T_f \\approx 126$ MeV.

Estimated current energy density of QCD axion dark matter.

Abstract

Visible matter in the current Universe is a consequence of the phase transition of the strong force, quantum chromodynamics (QCD). This phase transition has occurred at the Universe temperature around $T_c\simeq 165\,$MeV while it was expanding. Strongly interacting matter particles are quarks above $T_c$, while they are pions, protons and neutrons below $T_c$. The spin degrees of freedom 37 in the quark and gluon phase just above $T_c$ are converted to 3 (pions) after the phase transition. This phase transition might have been achieved mostly at supercooled temperatures. The supercooling was provided by the expansion of the Universe. We obtain the effective bubble formation rate $\alpha(T)\approx 10^{4-5}\,$MeV and the completion temperature of the phase change (to the hadronic phase), $T_f\simeq 126\,$MeV. During the phase transition, the scale factor $R$ has increased by a factor of 2.4. This provides a key knowledge on the energy density of "invisible" QCD axion at the full hadronic-phase commencement temperature $T_f$, and allows for us to estimate the current energy density of cold dark matter composed of "invisible" QCD axions.