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Sterile neutrinos with a mass in the eV range have been invoked as a possibleexplanation of a variety of short baseline (SBL) neutrino oscillationanomalies. However, if one considers neutrino oscillations between active andsterile neutrinos, such neutrinos would have been fully thermalised in theearly universe, and would be therefore in strong conflict with cosmologicalbounds. In this study we first update cosmological bounds on the mass andenergy density of eV-scale sterile neutrinos. We then perform an updated studyof a previously proposed model in which the sterile neutrino couples to a newlight pseudoscalar degree of freedom. Consistently with previous analyses, wefind that the model provides a good fit to all cosmological data and allows thehigh value of $H_0$ measured in the local universe to be consistent withmeasurements of the cosmic microwave background. However, new high $\ell$polarisation data constrain the sterile neutrino mass to be less thanapproximately 1 eV in this scenario. Finally, we combine the cosmologicalbounds on the pseudoscalar model with a Bayesian inference analysis of SBL dataand conclude that only a sterile mass in narrow ranges around 1 eV remainsconsistent with both cosmology and SBL data.

Sterile neutrino self-interactions: $H_0$ tension and short-baseline anomalies