Gravitational Wave Echo of Relaxion Trapping
  To solve the hierarchy problem, the relaxion must remain trapped in the
correct minimum, even if the electroweak symmetry is restored after reheating.
In this scenario, the relaxion starts rolling again until the backreaction
potential, with its set of local minima, reappears. Depending on the time of
barrier reappearance, Hubble friction alone may be insufficient to retrap the
relaxion in a large portion of the parameter space. Thus, an additional source
of friction is required, which might be provided by coupling to a dark
photon.The dark photon experiences a tachyonic instability as the relaxion
rolls, which slows down the relaxion by backreacting to its motion, and
efficiently creates anisotropies in the dark photon energy-momentum tensor,
sourcing gravitational waves. We calculate the spectrum of the resulting
gravitational wave background from this new mechanism, and evaluate its
observability by current and future experiments. We further investigate the
possibility that the coherently oscillating relaxion constitutes dark matter
and present the corresponding constraints from gravitational waves.
