The relaxion mechanism elegantly solves the Higgs hierarchy problem, but it requires that the early Universe experiences a long inflation phase with a small energy scale since the settle down of the relaxion needs to take place during inflation. In this paper, unlike the original one, we consider another scenario in which the Higgs vacuum expectation value is determined after inflation. To accomplish the mechanism, we take into account the effects of the Hubble-induced mass and thermal one in the dynamics of the relaxion. Then, we find that for the relaxion mechanism the coupling of the relaxion with the additional mass terms should be large.
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