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Considering the gauge model $SU(2)_L \times U(1)$ with the extension of the lepton sector by right-handed sterile Majorana neutrinos, we distinguish a "minimal parametric mixing scenario" for a complete matrix of $6 \times 6$ light (active) and sterile neutrinos, which depends, in addition to experimentally measured physical parameters, only on the masses of sterile neutrinos. For such a scenario, improved cosmological bounds are provided, resulting from the lifetime of sterile neutrinos and the fraction of energy carried by sterile neutrino dark matter.