Gravitational waves from axion-like particle cosmic string-wall networks

Axion-like particles (ALPs) are a compelling candidate for dark matter (DM), whose production is associated with the formation of a string-wall network. If walls bounded by strings persist, which requires the potential to have multiple local minima ($N>1$), they must annihilate before they become dominant. They annihilate mostly into gravitational waves and non-relativistic ALPs. We show that for ALPs other than the QCD axion these gravitational waves, if produced at temperatures below 100 eV, could be detected by future cosmological probes for ALPs with mass from $10^{-16}$ to $10^{6}$ eV that could constitute the entirety of the DM.