  We consider a dark sector model containing stable fermions charged under an
unbroken $U(1)$ gauge interaction, with a massless dark photon as force
carrier, and interacting with ordinary matter via scalar messengers. We study
its early Universe evolution by solving a set of coupled Boltzmann equations
that track the number density of the different species, as well as entropy and
energy exchanges between the dark and visible sectors. Phenomenologically
viable realizations include: i) a heavy (order 1 TeV or more) lepton-like dark
fermion playing the role of the dark matter candidate, with various production
mechanisms active depending on the strength of the dark-visible sector portal;
ii) light (few GeV to few tens of GeV) quark-like dark fermions, stable but
with suppressed relic densities; iii) an extra radiation component in Universe
due to dark photons, with temperature constrained by cosmic microwave
background data, and in turn preventing dark fermions to be lighter than about
1 GeV. Extra constraints on our scenario stem from dark matter direct detection
searches: the elastic scattering on nuclei is driven by dipole or charge radius
interactions mediated by either Standard Model or dark photons, providing
long-range effects which, however, are not always dominant, as usually assumed
in this context. Projected sensitivities for next-generation detectors cover a
significant portion of the viable parameter space and are competitive with
respect to the model-dependent constraints derived from the magnetic dipole
moments of leptons and cooling of stellar systems.
