  The increasing observational pressure on the standard cosmological model
motivates analyses going beyond the paradigm of the collision-less cold dark
matter (DM). Since the only clear evidence for the existence of DM is based on
gravitational interactions, it seems particularly fitting to study them in this
sector where extensions to the standard model can be naturally introduced. A
promising avenue can be obtained using modifications of the space-time metric
coupled 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 all
the matter species universally, including additional heavy DM particles. We
present a simple two-component DM model employing derivative conformal
interactions between the two DM species. This can simultaneously: 1) guarantee
the necessary symmetries to stabilize the dark species, 2) predict a
subdominant thermal relic density of the heavy DM component, and 3) alleviate
small-scale structure tensions of the cold DM scenario due to the possible
co-interactions in the dark sector. The scenario is highly predictive with
future observational prospects ranging from the Large Hadron Collider (LHC) to
gravitational-wave searches, and can be generalized to more rich and realistic
dark sector models.
