  We consider cosmological models where dark matter is charged under a dark
Abelian gauge field. This new interaction is repulsive and competes with
gravity on large scales and in the dynamics of galaxies and clusters. We focus
on non-linear models of dark electrodynamics where the effects of the new force
are screened within a K-mouflage radius that helps avoiding traditional
constraints on charged dark matter models. We discuss the background cosmology
of these models in a Newtonian approach and show the equivalence with
relativistic Lema\^itre models where an inhomogeneous pressure due to the
electrostatic interaction is present. In particular, we find that dark matter
shells of different radii evolve differently as they exit their K-mouflage
radii at different times, resulting in a breaking of the initial comoving
evolution. In the large time regime, the background cosmology is described by
comoving but inhomogeneous model with a reduced gravitational Newton constant
and a negative curvature originating from the electrostatic pressure. Baryons
do not directly feel the electrostatic interaction, but are influenced by the
inhomogeneous matter distribution induced by the electric force. We find that
shells of smaller radii evolve faster than the outer shells which feel the
repulsive interaction earlier. This mimics the discrepancy between the large
scale Hubble rate and the local one. Similarly, as galaxies and clusters are
not screened by the new interaction, large scale global flows would result from
the existence of the new dark electromagnetic interaction.
