Observing invisible axions with gravitational waves

If the Peccei-Quinn symmetry associated to an axion has ever been restored after inflation, axion strings inevitably produce a contribution to the stochastic gravitational wave background. Combining effective field theory analysis with numerical simulations, we show that the resulting gravitational wave spectrum has logarithmic deviations from a scale invariant form with an amplitude that is significantly enhanced at low frequencies. As a result, a single ultralight axion-like particle with a decay constant larger than 10(14) GeV and any mass between 10(-18) eV and 10(-28) eV leads to an observable gravitational wave spectrum and is compatible with constraints on the post-inflationary scenario from dark matter overproduction, isocurvature and dark radiation. Since the spectrum extends over a wide range of frequencies, the resulting signal could be detected by multiple experiments. We describe straightforward ways in which the Peccei-Quinn symmetry can be restored after inflation for such decay constants. We also comment on the recent possible NANOgrav signal in light of our results.

Automated summary

This study reveals that the restored Peccei-Quinn symmetry after inflation results in significantly enhanced gravitational wave spectrum at low frequencies produced by axion strings, which provides observational constraints on dark matter overproduction, isocurvature, and dark radiation scenarios. As a result, detectable gravitational wave signals could be generated by ultralight axion-like particles with suitable decay constants.