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 δ t = (10⁻⁸--10¹)\,s for the gauge boson masses mA' = (10⁻²³--10⁻¹⁹)\,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.