Self-interacting neutrinos: Solution to Hubble tension versus experimental constraints

Exotic self-interactions among the Standard Model neutrinos have been proposed as a potential reason behind the tension in the expansion rate, $H_0$, of the universe inferred from different observations. We constrain this proposal using electroweak precision observables, rare meson decays, and neutrinoless double-$β$ decay. In contrast to previous works, we emphasize the importance of carrying out this study in a framework with full Standard Model gauge invariance. We implement this first by working with a relevant set of Standard Model effective field theory operators and subsequently by considering a UV completion in the inverse seesaw model. We find that the scenario in which all flavors of neutrinos self-interact universally is strongly constrained, disfavoring a potential solution to the $H_0$ problem in this case. The scenario with self-interactions only among tau neutrinos is the least constrained and can potentially be consistent with a solution to the $H_0$ problem.