Gravitational wave production from axion rotations right after a transition to kination

Rotations of axion fields in the early Universe can produce dark matter and the matter-antimatter asymmetry of the Universe. We point out that the rotation can generate an observable amount of a stochastic gravitational wave (GW) background. It can be doubly enhanced in a class of models in which the equation of state of the rotations rapidly changes from a nonrelativistic matterlike one to a kinationlike one by (1) the so-called poltergeist mechanism and (2) slower redshift of GWs compared to the axion-kination fluid. In supersymmetric UV completion, future GW observations can probe the supersymmetry-breaking scale up to $10^7 GeV$ even if the axion does not directly couple to the Standard Model fields.