Light sterile neutrinos mixing with the active ones have been recently proposed to solve different anomalies observed in short-baseline oscillation experiments. These neutrinos can also be produced by oscillations of the active neutrinos in the early Universe, leaving possible traces on different cosmological observables. Here, we perform an updated study of the neutrino kinetic equations in ($3+1$) and ($2+1$) oscillation schemes, dynamically evolving primordial asymmetries of active neutrinos and taking into account for the first time $CP$-violation effects. In the absence of neutrino asymmetries, eV-mass scale sterile neutrinos would be completely thermalized, creating a tension with respect to the cosmic microwave background, large scale structures, and big bang nucleosynthesis data. In the past literature, active neutrino asymmetries have been invoked as a way to inhibit the sterile neutrino production via the in-medium suppression of the sterile-active mixing angle. However, neutrino asymmetries also permit a resonant sterile neutrino production. We find that if the active species have equal asymmetries $L$, a value $|L|={10}^{-3}$ is required to start suppressing the resonant sterile production, roughly an order of magnitude larger than what was previously expected. When active species have opposite asymmetries, the sterile abundance is further enhanced, requiring an even larger $|L|\simeq {10}^{-2}$ to start suppressing their production. In the latter case, $CP$ violation (naturally expected) further exacerbates the phenomenon. Some consequences for cosmological observables are briefly discussed: for example, it is likely that moderate suppressions of the sterile species production are associated with significant spectral distortions of the active neutrino species, with potentially interesting phenomenological consequences especially for big bang nucleosynthesis.

• Received 12 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.053009