The original mimetic model was proposed to take the role of dark matter. In this paper we consider possible direct interactions of the mimetic dark matter with other matter in the universe, especially the standard model particles such as baryons and photons. By imposing shift symmetry, the mimetic dark matter field can only have derivative couplings. We discuss the possibilities of generating baryon number asymmetry and cosmic birefringence in the universe based on the derivative couplings of the mimetic dark matter to baryons and photons.
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