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We show that relaxion models, that addresses the hierarchy problem, can naturally also account
for the observed dark matter (DM) relic density. The setup is similar to the case of axion DM
models with a dynamical- cosmological misalignment mechanism. After the reheating, when the
temperature is well above the electroweak scale, the back-reaction potential disappears and the
relaxion is displaced from its vacuum. When the "wiggles" reappears the relxion coherently oscillates
around its minima as in the case of vanilla axion dark matter models. We identify the parameter
space such that the relaxion is re-trapped leading to standard cosmology. When the relaxion is
light enough, below 10^{-4} eV, Hubble friction during radiation-domination is sufficiently strong for
re-trapping and even minimal model are "miraculously" found to be viable. It also leads to a new
constraints on relaxion models, as a sizeable region of their parameter space could lead to relaxion-
DM over abundance. 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 on the
one hand by a time-dependent axion-like field; where on the other hand, due to the fact that the
relaxion expectation value breaks CP, it mixes with the Higgs, at the same time its background
behaves as a time-dependent dilaton/scalar oscillating field. |