Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition

A large primordial lepton asymmetry can generate the observed baryon asymmetry of the Universe (BAU) through nonrestoration of electroweak symmetry at a high temperature, suppressing the sphaleron rate (“sphaleron freeze-in”). Such an asymmetry can lead to a first-order cosmic QCD transition with an observable gravitational wave (GW) signal. With next-to-leading order dimensional reduction and the exact 1-loop fluctuation determinant, we find the required lepton asymmetry to be an order of magnitude smaller than previous estimates. We apply a new and improved QCD equation of state reconciling the lattice and functional QCD results, to identify the range of lepton flavor asymmetries inducing a first-order cosmic QCD transition. Consistency with the observational constraints on the lepton asymmetries from the CMB and BBN requires an entropy dilution by a factor of $O\left(10\right)$ for the correct BAU, while the first-order QCD transition can itself occur without the need for any entropy dilution. We show that the sphaleron freeze-in paradigm can potentially be probed by future GW experiments like $\mu$Ares, if the bubble wall velocity of the QCD transition is large.