Cogenesis of baryon and dark matter with PBH and QCD axion

With entropy injection, an early matter-dominated epoch (EMD) impels the axion decay constant $f_a$ towards larger values to produce correct axion dark matter (DM) abundance, thereby unfolding the low-mass axion ($m_a\lesssim 10^{-5}$ eV) parameter space to be searched for in axion experiments. We implement this proposition in a scenario where $f_a$ and the leptogenesis scale in a seesaw mechanism are equivalent. We show, that if instead, the EMD is provided by evaporating ultralight primordial black holes (PBH), the scenario becomes strikingly testable with gravitational waves (GW) background alongside the axion searches. In particular, while being consistent with correct axion DM abundance, the scale $f_a\gtrsim 10^{12}$ GeV, corresponding to the unflavored regime of leptogenesis with hierarchical right-handed neutrinos, can be probed with GW and axion experiments, which is otherwise not testable at neutrino or collider experiments. Additionally, axions produced from PBH evaporation can give rise to dark radiation within reach of future cosmic microwave background experiments.