"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 $T_c\simeq 165\,$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.
