Chiral symmetry breaking and pion condensation in the early Universe

We determine the possible trajectories the Universe may have followed in the quantum chromodynamics (QCD) phase diagram during the QCD epoch. We focus on the roles of chiral symmetry breaking and pion condensation under high imbalances in lepton asymmetry. Adopting the quark-meson model as an effective description of QCD at finite temperature, charge and baryon chemical potentials we show that, for sufficiently large but physically motivated asymmetries, the Universe may have entered the pion condensation phase through a first-order phase transition, followed by a second-order phase transition when exiting it. Such a first-order phase transition represents a new possible source of primordial gravitational waves during the QCD epoch.