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We consider the recently proposed cosmological relaxation mechanism where thehierarchy problem is ameliorated, and the electroweak scale is dynamicallyselected by a slowly rolling axion field. We argue that, in its simplest form,the construction breaks a gauge symmetry that always exists forpseudo-Nambu-Goldstone bosons (in particular the axion). The small parameter inthe relaxion model is therefore not technically natural as it breaks a gaugesymmetry rather than global symmetries only. The consistency of the theorygenerically implies that the cutoff must lie around the electroweak scale, butnot qualitatively higher. We discuss several ways to evade the aboveconclusion. Some of them may be sufficient to increase the cutoff to thefew-TeV range (and therefore may be relevant for the little-hierarchy problem).To demonstrate the ideas in a concrete setting we consider a model with afamilon, the Nambu-Goldstone boson of a spontaneously broken chiral flavorsymmetry. The model has some interesting collider-physics aspects and containsa viable weakly interacting dark matter candidate.

Is the Relaxion an Axion?