Cosmic axion background

Existing searches for cosmic axions relics have relied heavily on the axion being non-relativistic and making up dark matter. However, light can be copiously produced in early Universe remain relativistic today, thereby constituting a Cosmic $\textit{axion}$ Background (C$a$B). As prototypical examples of sources, we consider thermal production, dark-matter decay, parametric resonance, topological defect decay. Each these has characteristic frequency spectrum that searched direct detection experiments. We focus axion-photon coupling study sensitivity current future versions ADMX, HAYSTAC, DMRadio, ABRACADABRA to C$a$B, finding data collected search matter repurposed detect energy densities well below limits set by measurements budget Universe. In this way, offers powerful new opportunity learn about and, potentially, discover axion.