Coherent relaxion dark matter

We show that relaxion, that addresses the hierarchy problem, can account for the observed dark matter (DM) relic density. The setup is similar to the case of axion DM models topped with a dynamical misalignment mechanism. After the reheating, when the temperature is well above the electroweak scale, the backreaction potential disappears and the relaxion is displaced from its vacuum. When the "wiggles" reappear the relaxion coherently oscillates around its minimum as in the case of vanilla axion DM models. We identify the parameter space such that the relaxion is retrapped leading to the standard cosmology. When the relaxion is lighter than $10^{-7}\,$eV, Hubble friction during radiation-domination is sufficiently strong for retrapping, and even minimal models are found to be viable. It also leads to a new constraint on relaxion models, as a certain region of their parameter space could lead to overabundant relaxion DM. Alternatively, even a larger parameter space exists when additional friction is obtained by particle production from additional coupling to an additional dark photon field. The phenomenology of this class of models is quite unique, as it implies that we are surrounded by a time-dependent axion-like field that due to relaxion-Higgs mixing implies time-dependent Higgs vacuum-expectation-value that lead to time-variation of all coupling constants of nature.