  We have recently shown that axions and axion-like particles (ALPs) may emit
an observable stochastic gravitational wave (GW) background when they begin to
oscillate in the early universe. In this note, we identify the regions of ALP
parameter space which may be probed by future GW detectors, including ground-
and space-based interferometers and pulsar timing arrays. Interestingly, these
experiments have the ability to probe axions from the bottom up, i.e. in the
very weakly coupled regime which is otherwise unconstrained. Furthermore, we
discuss the effects of finite dark photon mass and kinetic mixing on the
mechanism, as well as the (in)sensitivity to couplings of the axion to Standard
Model fields. We conclude that realistic axion and ALP scenarios may indeed be
probed by GW experiments in the future, and provide signal templates for
further studies.
