Cosmology with a Non-minimally Coupled Dark Matter Fluid II. Cosmological Perturbations

Abstract

We extend our study of a cosmological scenario in which dark matter is non-minimally coupled to gravity at the fluid level. In previous work, we showed that this interaction can drive an early phase of accelerated expansion, addressing the horizon and flatness problems, and can also lead to a cosmological bounce in the presence of spatial curvature. Here we analyse the evolution of linear perturbations in this framework. We derive the equations governing scalar, vector and tensor perturbations, and obtain analytic solutions in the relevant cosmological regimes. We find that perturbations generated during the accelerated expansion phase produce a strongly blue scalar power spectrum and are therefore incompatible with observations. By contrast, in bouncing solutions primordial fluctuations can originate during the contracting phase before the bounce. In this case, the model yields an approximately scale-invariant scalar power spectrum while keeping the tensor-to-scalar ratio compatible with current bounds, without introducing additional scalar fields. Although our treatment relies on simplifying approximations that should be refined in future work, these results indicate that non-minimally coupled dark matter may provide a viable alternative mechanism for the generation of primordial cosmological perturbations.