Constraining the Self-Interacting Neutrino Interpretation of the Hubble Tension

Large, nonstandard neutrino self-interactions have been shown to resolve the ∼4σ tension in Hubble constant measurements and a milder tension in the amplitude of matter fluctuations. We demonstrate that interactions of the necessary size imply the existence of a force carrier with a large neutrino coupling (>10^{-4}) and mass in the keV-100 MeV range. This mediator is subject to stringent cosmological and laboratory bounds, and we find that nearly all realizations of such a particle are excluded by existing data unless it carries spin 0 and couples almost exclusively to τ-flavored neutrinos. Furthermore, we find that the light neutrinos must be Majorana particles, and that a UV-complete model requires a nonminimal mechanism to simultaneously generate neutrino masses and appreciable self-interactions.