Vector Fuzzy Dark Matter, Fifth Forces, and Binary Pulsars
  We study the secular effects that an oscillating background ultralight
(fuzzy) cosmological vector field has on the dynamics of binary systems; such
effects appear when the field and the binary are in resonance. We first
consider the gravitational interaction between the field and the systems, and
quantify the main differences with an oscillating background scalar field. If
the energy density of such a field is sufficiently large, as required if it is
supposed to be all of the dark matter, we show that the secular effects could
yield potentially observable signatures in high precision time of arrival
measurements of binary pulsars. We then analyse the secular effects that arise
when the field is directly coupled to the bodies in the binary. We show that
this study is particularly relevant for models where fuzzy dark matter mediates
a baryonic force $B$ (or $B-L$, with $L$ the lepton number), due to the stellar
amount of nucleons present in the stars. The constraints we obtain from current
data are already competitive with (or even more constraining than) laboratory
tests of the equivalence principle.
