  The lepton flavour asymmetries of the Universe are observationally almost
unconstrained before the onset of neutrino oscillations. We calculate the
cosmic trajectory during the cosmic QCD epoch in the presence of large lepton
flavour asymmetries. By including QCD thermodynamic quantities derived from
functional QCD methods in our calculation our work reveals for the first time
the possibility of a first-order cosmic QCD transition. We specify the required
values of the lepton flavour asymmetries for which a first-order transition
occurs for a number of different benchmark scenarios.
