Unveiling dark fifth forces with linear cosmology

We initiate the exploration of the cosmology of dark fifth forces: new forces acting solely on Dark Matter. We focus on long range interactions which lead to an effective violation of the Equivalence Principle on cosmological scales today. At the microscopic level, the dark fifth force can be realized by a light scalar with mass smaller than the Hubble constant today (≲ 10$^{-33}$ eV) coupled to Dark Matter. We study the behavior of the background cosmology and linear perturbations in such a Universe. At the background level, the new force modifies the evolution of the Dark Matter energy density and thus the Hubble flow. At linear order, it modifies the growth of matter perturbations and generates relative density and velocity perturbations between Dark Matter and baryons that grow over time. We derive constraints from current CMB and BAO data, bounding the strength of the dark fifth force to be less than a percent of gravity. These are the strongest constraints to date. We present potential implications of this scenario for the Hubble tension and discuss how our results are modified if the light scalar mediator accounts for the observed density of the Dark Energy. Finally, we comment on the interplay between our constraints and searches for violations of the Equivalence Principle in the visible sector.