A possible interpretation of the Higgs mass by the cosmological attractive relaxion

Recently, a novel idea has been proposed to relax the electroweak hierarchy problem through the cosmological inflation and the axion periodic potential. Here, we further assume that only the attractive inflation is needed to explain the light mass of the Higgs boson, where we do not need a specified periodic potential of the axion field. Attractive inflation during the early universe drives the Higgs boson mass from the large value in the early universe to the small value at present, where the Higgs mass is an evolving parameter of the Universe. Thus, the small Higgs mass can technically originate from the cosmological evolution rather than dynamical symmetry or anthropics. Further, we study the possible collider signals or constraints at future lepton collier and the possible constraints from the muon anomalous magnetic moment. A concrete attractive relaxion model is also discussed, which is consistent with the data of Planck 2015.