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Collisional production of sterile neutrinos via secret interactions and cosmological implications

Secret interactions among sterile neutrinos have been recently proposed as an escape-route to reconcile eV sterile neutrino hints from short-baseline anomalies with cosmological observations. In particular models with coupling g_X \gtrsim 10^{-2} and gauge boson mediators $X$ with $M_X \lesssim 10$ MeV lead to large matter potential suppressing the sterile neutrino production before the neutrino decoupling. With this choice of parameter ranges, big bang nucleosynthesis is left unchanged and gives no bound on the model. However, we show that at lower temperatures when active-sterile oscillations are no longer matter suppressed, sterile neutrinos are still in a collisional regime, due to their secret self-interactions. The interplay between vacuum oscillations and collisions leads to a scattering-induced decoherent production of sterile neutrinos with a fast rate. This process is responsible for a flavor equilibration among the different neutrino species. We explore the effect of this large sterile neutrino population on cosmological observables. We find that a signature of strong secret interactions would be a reduction of the effective number of neutrinos $N_{\rm eff}$ at matter radiation equality down to 2.7. Moreover, for $M_X \gtrsim g_X$ MeV sterile neutrinos would be free-streaming before becoming non-relativistic and they would affect the large-scale structure power spectrum. As a consequence, for this range of parameters we find a tension of a eV mass sterile state with cosmological neutrino mass bounds.