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 $\delta t = \left(10^{-8}-10^1\right)\,$s for the gauge boson masses $m_{A'} = \left(10^{-23}-10^{-19}\right)\,$eV and the coupling with the neutrino $g= 10^{-27}-10^{-20}$. 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.