Cosmological CP -odd axion field as the coherent Berry’s phase of the Universe

Abstract

We consider a dark matter (DM) model offering a very natural explanation of the observed relation, $\Omega_{\rm dark} \sim \Omega_{\rm visible}$. This generic consequence of the model is a result of the common origin of both types of matter (DM and visible) which are formed during the same QCD transition. The masses of both types of matter in this framework are proportional to one and the same dimensional parameter of the system, $\Lambda_{\rm QCD}$. The focus of the present work is the detail study of the dynamics of the $\cal{CP}$-odd coherent axion field $a(x)$ just before the QCD transition. We argue that the baryon charge separation effect on the largest possible scales inevitably occurs as a result of merely existence of the coherent axion field in early Universe. It leads to preferential formation of one species of nuggets on the scales of the visible Universe where the axion field $a(x)$ is coherent. A natural outcome of this preferential evolution is that only one type of the visible baryons remains in the system after the nuggets complete their formation. This represents a specific mechanism on how the baryon charge separation mechanism (when the Universe is neutral, but visible part of matter consists the baryons only) replaces the conventional "baryogenesis" scenarios.