  The nature of dark matter is a problem with too many potential solutions. We
investigate whether a consistent embedding into quantum gravity can decimate
the number of solutions to the dark-matter problem. Concretely, we focus on a
hidden sector composed of a gauge field and a charged scalar, with gauge group
U(1)$_{\textmd{D}}$ or SU(2)$_\textmd{D}$. The gauge field is the dark matter
candidate, if the gauge symmetry is broken spontaneously. Phenomenological
constraints on the couplings in this model arise from requiring that the
correct dark matter relic density is produced via thermal freeze-out and that
recent bounds from direct-detection experiments are respected. We find that the
consistent embedding into asymptotically safe quantum gravity gives rise to
additional constraints on the couplings at the Planck scale, from which we
calculate corresponding constraints at low energy scales. We discover that
phenomenological constraints cannot be satisfied simultaneously with
theoretical constraints from asymptotically safe quantum gravity, ruling out
these dark matter models.
