Baryogenesis, Primordial Black Holes and MHz-GHz Gravitational Waves

Gravitational waves (GWs) in the MHz - GHz frequency range are motivated by a host of early Universe phenomena such as oscillons, preheating, and cosmic strings. We point out that baryogenesis too serves as a motivation to probe GWs in this frequency range. The connection is through primordial black holes (PBHs): on the one hand, PBHs induce baryogenesis by Hawking evaporating into a species that has baryon number and $CP$ violating decays; on the other, PBHs induce GWs through second order effects when the scalar fluctuations responsible for their formation re-enter the horizon. We describe the interplay of the parameters responsible for successful baryogenesis on the plane of the strain and frequency of the induced GWs, being careful to delineate regimes where PBH domination or washout effects occur. We provide semi-analytic scalings of the GW strain with the baryon number to entropy ratio and other parameters important for baryogenesis. Along the way, we sketch a solution to the dark matter-baryogenesis coincidence problem with two populations of PBHs, which leads to a double-peaked GW signal. Our results underscore the importance of probing the ultra high frequency GW frontier.