“…The dark sector of our Universe may be more featured than the conventional picture of weakly interacting CDM particles and neutrinos. For instance, the possibility of nonminimal interactions of dark matter have been intensely investigated in the literature from different motivations and perspectives, e.g., dark matter interaction with DE [23][24][25], neutrinos [26,27], baryons [28][29][30], photons [31,32] and dark radiation [33,34]. In this paper, we follow a novel approach assuming that CDM and relativistic relics (neutrinos and any other relativistic relics) are interacting only gravitationally and have the conventional intrinsic properties, namely, have the equations of state as usual as p = 0 and p/ρ = 1/3, respectively, but couple to the spacetime in accordance with a modified gravity, namely, the scale-independent energy-momentum squared gravity, which allows different gravitational couplings for the different species of the sources, and thereby induces a pseudo nonminimal interaction of each species culminating in modifications at the background and perturbative levels.…”