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Axion field and the quark nugget's formation at the QCD phase transition

We study a testable dark matter (DM) model outside of the standard WIMP paradigm in which the observed ratio $Ω_{\rm dark} \simeq Ω_{\rm visible}$ for visible and dark matter densities finds its natural explanation as a result of their common QCD origin when both types of matter (DM and visible) are formed at the QCD phase transition and both are proportional to $Λ_{\rm QCD}$. Instead of conventional "baryogenesis" mechanism we advocate a paradigm when the "baryogenesis" is actually a charge separation process which always occur in the presence of the $\cal{CP}$ odd axion field $a(x)$. In this scenario the global baryon number of the Universe remains zero, while the unobserved anti-baryon charge is hidden in form of heavy nuggets, similar to Witten's strangelets and compromise the DM of the Universe. We argue that the nuggets will be inevitably produced during the QCD phase transition as a result of Kibble-Zurek mechanism on formation of the topological defects during a phase transition. Relevant topological defects in our scenario are the closed bubbles made of the $N_{\rm DW}=1$ axion domain walls. These bubbles, in general, accrete the baryon (or anti baryon) charge, which eventually result in formation of the nuggets and anti-nuggets carrying a huge baryon (anti-baryon) charge. The main consequence of the model, $Ω_{\rm dark} \approx Ω_{\rm visible}$ is insensitive to the axion mass which may assume any value within the observationally allowed window $10^{-6} {\rm eV} \lesssim m_a \lesssim 10^{-3}{\rm eV}$. We also estimate the baryon to entropy ratio $η\equiv {n_B}/{n_γ}\sim 10^{-10}$ within this scenario. Finally, we comment on implications of these results to the axion search experiments, including microwave cavity and the Orpheus experiments.