Catastrogenesis: DM, GWs, and PBHs from ALP string-wall networks

Axion-like particles (ALPs), a compelling candidate for dark matter (DM), are the pseudo Nambu-Goldstone bosons of a spontaneously and explicitly broken global $U(1)$ symmetry. When the symmetry breaking happens after inflation, the ALP cosmology predicts the formation of a string-wall network which must annihilate early enough, producing gravitational waves (GWs) and primordial black holes (PBHs), as well as non-relativistic ALPs. We call this process catastrogenesis. We show that, under the generic assumption that the potential has several degenerate minima, GWs from string-wall annihilation at temperatures below 100 eV could be detected by future CMB and astrometry probes, for ALPs with mass from $10^{-16}$ to $10^{6}\,\rm eV$. In this case, structure formation could limit ALPs to constitute a fraction of the DM and the annihilation would produce mostly ``stupendously large" PBHs. For larger annihilation temperatures, ALPs can constitute $100\%$ of DM, and the annihilation could produce supermassive black holes with a mass of up to $10^9\, M_\odot$ as found at the center of large galaxies. Therefore our model could solve two mysteries, the nature of the DM and the origin of these black holes.