Pion condensation in the early Universe at nonvanishing lepton flavor
  asymmetry and its gravitational wave signatures
  We investigate the possible formation of a Bose-Einstein condensed phase of
pions in the early Universe at nonvanishing values of lepton flavor
asymmetries. A hadron resonance gas model with pion interactions, based on
first-principle lattice QCD simulations at nonzero isospin density, is used to
evaluate cosmic trajectories at various values of electron, muon, and tau
lepton asymmetries that satisfy the available constraints on the total lepton
asymmetry. The cosmic trajectory can pass through the pion condensed phase if
the combined electron and muon asymmetry is sufficiently large: $|l_e +
l_{\mu}| \gtrsim 0.1$, with little sensitivity to the difference $l_e - l_\mu$
between the individual flavor asymmetries. Future constraints on the values of
the individual lepton flavor asymmetries will thus be able to either confirm or
rule out the condensation of pions during the cosmic QCD epoch. We demonstrate
that the pion condensed phase leaves an imprint both on the spectrum of
primordial gravitational waves and on the mass distribution of primordial black
holes at the QCD scale e.g. the black hole binary of recent LIGO event GW190521
can be formed in that phase.
