Baryogenesis and first-order QCD transition with gravitational waves from a large lepton asymmetry

Abstract: A large primordial lepton asymmetry can lead to successful baryogenesis by preventing the restoration of electroweak symmetry at high temperatures, thereby suppressing the sphaleron rate. This asymmetry can also lead to a first-order cosmic QCD transition, accompanied by detectable gravitational wave (GW) signals. By employing next-to-leading order dimensional reduction we determine that the necessary lepton asymmetry is approximately one order of magnitude smaller than previously estimated. Incorporating an updated QCD equation of state that harmonizes lattice and functional QCD outcomes, we pinpoint the range of lepton flavor asymmetries capable of inducing a first-order cosmic QCD transition. To maintain consistency with observational constraints from the Cosmic Microwave Background and Big Bang Nucleosynthesis, achieving the correct baryon asymmetry requires entropy dilution by approximately a factor of ten. However, the first-order QCD transition itself can occur independently of entropy dilution. We propose that the sphaleron freeze-in mechanism can be investigated through forthcoming GW experiments such as $\mu$Ares.