We studied nonequilibrium oscillations between left-handed electron neutrinos and nonthermalized sterile neutrinos. The exact kinetic equations for neutrinos, written in terms of neutrino density matrix in momentum space were analyzed. The evolution of neutrino density matrix was numerically calculated. This allowed to study precisely the evolution of the neutrino number densities, energy spectrum distortion and the asymmetry between neutrinos and antineutrinos for each momentum mode. Both effects of distortion and asymmetry, which cannot be accounted for correctly when working in terms of particle densities and mean energies, and the depletion of electron neutrino state have been proved considerable for a certain range of oscillation parameters. The influence of nonequilibrium oscillations on primordial nucleosynthesis was calculated. Cosmologically excluded regions for oscillation parameters were obtained. Nonequilibrium neutrino oscillationsWe discuss nonequilibrium oscillations between weak interacting electron neutrinos ν e and sterile neutrinos ν s for the case when ν s do not thermalize till 2 M eV and oscillations become effective after ν e decoupling. Oscillations of that type, but for the case of ν s thermalizing before or around 2 M eV have been already discussed in literature. 1−8 We have provided a proper kinetic analysis of the neutrino evolution in terms of kinetic equations for the neutrino density matrix in momentum space. The assumptions of the model are the following: (a) Singlet neutrinos decouple much earlier than the active neutrinos do: T F νs ≥ T F νe , therefore, in later epochs T νs ≤ T νe , due to the additional heating of ν e in equilibrium in comparison with the already decoupled ν s . Hence, the number densities of ν s are considerably less than those of ν e , N νs << N νe . (b)We consider oscillations between ν s and ν e , according to the Majorana&Dirac mixing scheme 9 with mixing present just in the electron

Possible modifications of the standard big-bang nucleosynthesis scenario, which would loosen the bound on the number of neutrino flavors, are examined. A concrete model with light ((mx=O( MeV )) quasistable particles (τx~1 s ) decaying into [Formula: see text] is considered. If the decay products do not thermalize they shift the frozen neutron-to-proton ratio and respectively the abundance of the light element produced primordially. The direction of this shift depends on the parameters of the model. Correspondingly for the particular choice of these parameters the restrictions on the number of neutrino flavors may be considerably weakened.

We study the nonresonant oscillations between left-handed electron neutrinos e and nonthermalized sterile neutrinos s in the early Universe plasma. The case when s do not thermalize until 2 MeV and the oscillations become effective after e decoupling is discussed. As far as for this model the rates of the expansion of the Universe, neutrino oscillations, and neutrino interactions with the medium may be comparable, we have analyzed the kinetic equations for the neutrino density matrix, accounting simultaneously for these processes. The evolution of neutrino ensembles was described numerically by integrating the kinetic equations for the neutrino density matrix in momentum space for small mass differences ␦m 2 р10 Ϫ7 eV 2 . This approach allowed us to study precisely the evolution of the neutrino number densities, energy spectrum distortion, and the asymmetry between neutrinos and antineutrinos due to oscillations for each momentum mode. We have performed a complete numerical analysis for the full range of the oscillations parameters of the model of the influence of the nonequilibrium e ↔ s oscillations on the primordial production of 4 He. The exact kinetic approach enabled us to calculate the effects of neutrino population depletion, the distortion of the neutrino spectrum, and the generation of neutrino-antineutrino asymmetry on the kinetics of neutron-to-proton transitions during the primordial nucleosynthesis epoch and correspondingly on cosmological 4 He production. It was shown that the neutrino population depletion and spectrum distortion play an important role. The asymmetry effect, in case the lepton asymmetry is accepted initially equal to the baryon one, is proved to be negligible for the discussed range of ␦m 2 . Constant helium contours in the ␦m 2 -plane were calculated. Thanks to the exact kinetic approach more precise cosmological constraints on the mixing parameters were obtained. ͓S0556-2821͑98͒04115-0͔ PACS number͑s͒: 14.60.Pq, 05.70.Ln, 26.35.ϩc of Sciences, blvd. Tsarigradsko

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In this work we present the results of our numerical analysis of the effect of lepton asymmetries L on neutrino oscillations and consequently on helium production in a model of cosmological nucleosynthesis with active-sterile neutrino oscillations. We performed detail calculations of the neutron-proton ratio till its freezing and the subsequent synthesis of helium-4 for a wide range of values of the initial lepton asymmetry 10 −4 − 10 −10 and for the complete set of mixing parameters of the oscillation model described in [1]: δm 2 ≤ 10 −7 eV 2 and any ϑ.We have found that there are significant modifications of neutrino number densities and energy distributions over a large range of values of the initial asymmetry. Hence, the previously derived (for the case of lepton asymmetry of the order of the baryon one) nucleosynthesis limits on the oscillation parameters are considerably altered. We have calculated the dependence of primordially produced helium-4 on the parameters of the model Yp(L, δm 2 , ϑ). From the isohelium contours in the δm 2 − ϑ plane, we have obtained limits on the neutrino mixing parameters corresponding to nucleosynthesis with degenerate neutrinos. An intriguing new result of our analysis is that the lepton asymmetry is able to tighten the nucleosynthesis bounds on neutrino mixing parameters, besides its well known ability to relax them.