Constraining postinflationary axions with pulsar timing arrays

Models that produce axionlike particles (ALPs) after cosmological inflation due to spontaneous U (1) symmetry breaking also produce cosmic-string networks. Those axionic strings lose energy through gravitational-wave emission during the whole cosmological history, generating a stochastic background of gravitational waves that spans many decades in frequency. We can therefore constrain the axion decay constant and axion mass from limits on the gravitational-wave spectrum and compatibility with dark matter abundance as well as dark radiation. We derive such limits from analyzing the most recent NANOGrav data from pulsar timing arrays (PTAs). The limits are similar to the N₄₅₅ bounds on dark radiation for ALP masses m₀10^-22 eV. On the other hand, for heavy ALPs with m₀0. 1 GeV and N₃ₖ1, new regions of parameter space can be probed by PTA data due to the dominant domain-wall contribution to the gravitational-wave background.