“Invisible” QCD axion rolling through the QCD phase transition

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 Tc≃165 MeV while it was expanding. Strongly interacting matter particles are quarks above Tc, while they are pions, protons and neutrons below Tc. The spin degrees of freedom 37 (u and d quarks and gluons) just above Tc 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 α(T)≈104−5 MeV and the completion temperature of the phase change (to the hadronic phase), Tf≃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 Tf, and allows for us to estimate the current energy density of cold dark matter composed of “invisible” QCD axions.