Weakening gravity for dark matter in a type-II minimally modified gravity

Abstract We propose a new cosmological framework in which the strength of gravitational force acted on dark matter at late time can be weaker than that standard fields without introducing extra degrees freedom. The integrates into type-II minimally modified gravity was recently proposed as energy mimicker. idea makes such possible consists coupling Lagrangian and constant to metric canonically transformed frame general relativity (GR). On imposing gauge fixing constraint, explicitly breaks temporal diffeomorphism invariance, we keep number freedom two, GR. then make inverse canonical transformation bring theory back original frame, where one add fields. This contains two free functions specify generating functional above mentioned are used order realize desired evolutions both Hubble expansion rate H(z) effective for G eff (z). aim this paper is therefore provide address puzzles present today's cosmology, i.e. H 0 tension S 8 tension, simultaneously. When cold framework, dub corresponding model V Canonical Cold Dark Matter (VCCDM), ? ?CDM replaced by function V(?) an auxiliary field ? CDM coupled frame.