Reentrant pion superfluidity and cosmic trajectories within PNJL model

TL;DR

This paper investigates charged pion superfluidity and cosmic trajectories in the early Universe using the PNJL model, revealing phase boundaries and chemical potential behaviors relevant to cosmological evolution.

Contribution

It provides a self-consistent analysis of pion superfluidity boundaries and cosmic trajectories within the PNJL model, incorporating lepton flavor asymmetries as free parameters.

Findings

Pion superfluidity phase boundary near the pseudocritical temperature.

Strong reaction of electric chemical potential at phase boundaries.

Cosmic trajectories show distinct responses of chemical potentials.

Abstract

In this work, we self-consistently explore the possibility of charged pion superfluidity and cosmic trajectories in early Universe under the framework of Polyakov-Nambu--Jona-Lasinio model. By taking the badly constrained lepton flavor asymmetries $l_{\rm e}$ and $l_\mu$ as free parameters, the upper boundaries of pion superfluidity phase are consistently found to be around the pseudocritical temperature at zero chemical potentials. So the results greatly support the choice of $T=0.16~{\rm GeV}$ as the upper boundary of pion superfluidity in the previous lattice QCD study. Take $l_{\rm e}+l_\mu=-0.2$ as an example, we demonstrate the features of pion condensation and the associated cosmic trajectories with the evolution of early Universe. While the trajectory of electric chemical potential reacts strongly at both the lower and upper boundaries of reentrant pion superfluidity, the trajectories of other chemical potentials only respond strongly at the upper boundary.