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The increasing observational pressure on the standard cosmological modelmotivates analyses going beyond the paradigm of the collision-less cold darkmatter (DM). Since the only clear evidence for the existence of DM is based ongravitational interactions, it seems particularly fitting to study them in thissector where extensions to the standard model can be naturally introduced. Apromising avenue can be obtained using modifications of the space-time metriccoupled to DM and induced by the presence of a new ultra-light scalar field$\phi$. The $\phi$ field can contribute to the DM density and can couple allthe matter species universally, including additional heavy DM particles. Wepresent a simple two-component DM model employing derivative conformalinteractions between the two DM species. This can simultaneously: 1) guaranteethe necessary symmetries to stabilize the dark species, 2) predict asubdominant thermal relic density of the heavy DM component, and 3) alleviatesmall-scale structure tensions of the cold DM scenario due to the possibleco-interactions in the dark sector. The scenario is highly predictive withfuture observational prospects ranging from the Large Hadron Collider (LHC) togravitational-wave searches, and can be generalized to more rich and realisticdark sector models.

Co-interacting dark matter and conformally coupled light scalars