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We introduce an oscillating scalar field coupled to the Higgs that canaccount for all dark matter in the Universe. Due to an underlying scaleinvariance of this model, the dark scalar only acquires mass after theelectroweak phase transition. We discuss the dynamics of this dark mattercandidate, showing that it behaves like dark radiation until the Electroweakphase transition and like non-relativistic matter afterwards. In the case of anegative coupling to the Higgs field, the scalar gets a vacuum expectationvalue after the electroweak phase transition and may decay into photons,although being sufficiently long-lived to account for dark matter. We showthat, within this scenario, for a mass of 7 keV, the model can explain theobserved galactic and extra-galactic 3.5 keV X-ray line. Nevertheless, it willbe very difficult to probe this model in the laboratory in the near future.

Scale-invariant scalar field dark matter through the Higgs portal