More Is Different: Reconciling eV Sterile Neutrinos with Cosmological Mass Bounds

It is generally expected that adding light sterile species would increase the effective number of neutrinos, $N_{eff}$. In this paper we discuss a scenario that $N_{eff}$ can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile species can be reached after big bang nucleosynthesis (BBN) epoch, but leading to a decrease of $N_{eff}$. In such a scenario, we also show that the conflict with cosmological mass bounds on the additional sterile neutrinos can be relaxed further when more light species are introduced.