Existing searches for cosmic axions relics have relied heavily on the axion being non-relativistic and making up dark matter. However, light axions can be copiously produced in the early Universe and remain relativistic today, thereby constituting a Cosmic $textit{axion}$ Background (C$a$B). As prototypical examples of axion sources, we consider thermal production, dark-matter decay, parametric resonance, and topological defect decay. Each of these has a characteristic frequency spectrum that can be searched for in axion direct detection experiments. We focus on the axion-photon coupling and study the sensitivity of current and futu
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