  In this paper we consider very weakly interacting and ultra light scalar and
pseudoscalar dark matter candidates. We show that quantum gravity has important
implications for such models and that the masses of the singlet scalar and
pseudoscalar fields must be heavier than $3\times 10^{-3}$ eV. However, if they
are gauged, their masses could be much lighter and as light as $10^{-22}\, {\rm
eV}$. The existence of new gauge forces in the dark matter sector can thus be
probed by atomic clocks or quantum sensors experiments.

High Energy Physics - Phenomenology;High Energy Physics - Theory