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. At
the microscopic level, the dark fifth force can be realized by a light scalar
with mass smaller than the Hubble constant today ($\lesssim
10^{-33}\,\text{eV}$) 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.
