Do neutrinos bend? Consequences of an ultralight gauge field as dark matter

An ultralight gauge boson could address the missing cosmic dark matter, with its transverse modes contributing to a relevant component of the galactic halo today. We show that, in the presence of a coupling between the gauge boson and neutrinos, these transverse modes affect the propagation of neutrinos in the galactic core. Neutrinos emitted from galactic or extra-galactic supernovae could be delayed by $\delta t=\left(10^{-8}\text{–}10^1\right)$  s for the gauge boson masses $m_{A^{\prime }}=\left(10^{-23}\text{–}10^{-19}\right)$  eV and the coupling with the neutrino $g=10^{-27}\text{–}10^{-20}$. While we do not focus on a specific formation mechanism for the gauge boson as the dark matter in the early Universe, we comment on some possible realizations. We discuss model-dependent current bounds on the gauge coupling from fifth-force experiments, as well as future explorations involving supernovae neutrinos. We consider the concrete case of the DUNE facility, where the coupling can be tested down to $g\simeq 10^{-27}$ for neutrinos coming from a supernova event at a distance $d=10$  kpc from Earth.