  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 CMB, LSS and BBN 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 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 BBN.
