Relaxion Fluctuations (Self-stopping Relaxion) and Overview of Relaxion
  Stopping Mechanisms
  In implementations of the electroweak scale cosmological relaxation mechanism
proposed so far, the effect of the quantum fluctuations of the homogeneous
relaxion field has been ignored. We show that they can grow during the
classical cosmological evolution of the relaxion field passing through its many
potential barriers. The resulting production of relaxion particles can act as
an efficient stopping mechanism for the relaxion. We revisit the original
relaxion proposal and determine under which conditions inflation may no longer
be needed as a source of friction. We review alternative stopping mechanisms
and determine in detail the allowed parameter space for each of them (whether
happening before, during and after inflation), also considering and severely
constraining the case of friction from electroweak gauge boson production in
models with large and Higgs-independent barriers.
