Cosmic QCD transition: From quark to strangeon nugget and nucleon?

We investigate a crossover quantum chromodynamical (QCD) phase transition that occurred in the early Universe and explore a potential formation scenario for stable strangeon nuggets during this process. To analyze the thermodynamics of the QCD phase involving u, d, s quarks, we employ the Polyakov-Nambu-Jona-Lasinio model, while the relativistic mean-field model is used to describe the hadronic matter. We consider the participation of strangeons (strange quark clusters with net strangeness) in the quark-hadron phase transition process. During this process, strangeon nuggets are formed, and larger nuggets could survive after the phase transition. The crossover phase transition from quarks to hadrons occur at a cosmic temperature of approximately T similar to 170MeV, and these two phases (quark phase and strangeon nugget-hadronic phase) are connected in a three-window model. We introduce a distribution function of the nugget baryon number, A, to describe the nugget's number density (equivalent to the mass spectrum). All strangeon nuggets with A>A(c) are considered to be stable, where the critical number, A(c), is determined by both weak and strong interactions. To calculate the thermodynamics of stable strangeon nuggets, a nonrelativistic equation of state was applied, resulting in negligible thermodynamic contributions (pressure, entropy, etc.) compared to the hadronic part. Our study shows that the mass fraction of the strangeon nuggets that survived from the early Universe is comparable to dark matter, suggesting a possible explanation for cold dark matter without introducing any exotic particles beyond the Standard Model.