Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry

We investigate how a lepton asymmetry impacts the cosmic trajectory in the QCD phase diagram. We study the evolution of chemical potentials during the QCD epoch of the early Universe using susceptibilities from lattice QCD to interpolate between an ideal quark gas and an ideal hadron resonance gas. The lepton asymmetry affects the evolution of all chemical potentials. The standard cosmic trajectory is obtained assuming tiny lepton and baryon asymmetries. For larger lepton asymmetry, the charge chemical potential exceeds the baryon chemical potential before pion annihilation.

Figure 1

Temperature evolution of chemical potentials for different negative total lepton asymmetries $l$. (Top) Baryon chemical potential ${\mu }_B$. (Middle) Electric charge chemical potential $-{\mu }_Q$. (Bottom) Electron lepton flavor chemical potential $-{\mu }_{L_e}$. Continuous lines for high temperatures are results for the ideal quark gas, for low temperatures for the HRG. The symbols (circle) and (triangle) indicate results obtained by using $2+1$ and $2+1+1$ flavor lattice QCD susceptibilities, respectively. The magnitude of the lepton asymmetry increases from left to right. The pseudocritical temperature $T_{\mathrm{QCD}}\approx 154\mathrm{MeV}$ is displayed by a horizontal dotted line. The standard cosmic trajectory of the early Universe is given by $l=-(51/28)b$.

Figure 2

Temperature evolution of baryon chemical potential ${\mu }_B$ and electric charge chemical potential ${\mu }_Q$ for both signs of a large lepton asymmetry. Continuous and dashed lines for high temperatures are results for the ideal quark gas, for low temperatures for the HRG. The symbols (circle) and (triangle) indicate results obtained by using $2+1$ and $2+1+1$ flavor lattice QCD susceptibilities, respectively.