Primordial Asymmetries, Primordial Equation of State & Primordial Black Holes

We study the thermal history of the primordial Universe in presence of non-zero lepton and baryon asymmetries. Considering different scenarios, we determine the equation of state (EoS) of the Universe from T = 10 GeV down to T = 1 keV, spanning the QCD transition, hadron gas phase and neutrino decoupling epochs. Using a combination of numerical codes, we track the cosmic trajectories of chemical potentials associated with the baryonic, leptonic and electric charges, and follow the evolution of lepton asymmetries including through the era where neutrino oscillations take place. Combining peak theory with numerical-relativity simulations of the collapse threshold, we show the EoS-induced modifications to the primordial black hole (PBH) mass spectrum. We determine the associated Gravitational Wave (GW) signal, showing how lepton asymmetries and a particular spectral index of curvature perturbations can be hinted at by current ground interferometer-based GW observations. Finally, we discuss constraints and positive evidence for PBHs.