| Summary: | We use Big Bang Nucleosynthesis (BBN) to probe Beyond Standard Model physics in the neutrino sector. Recently, the abundances of primordially produced light elements D and He-4 were determined from observations with better accuracy. The good agreement between the theoretically predicted abundances of primordially produced light elements and those derived from observations allows us to update the BBN constraints on Beyond Standard Model (BSM) physics. We provide numerical analysis of several BSM models of BBN and obtain precise cosmological constraints and indications for new neutrino physics. Namely, we derive more stringent BBN constraints on electron neutrino–sterile neutrino oscillations corresponding to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> uncertainty of the observational determination of the primordial He-4. The cosmological constraints are obtained both for the zero and non-zero cases of the initial population of the sterile neutrino state. Then, in a degenerate BBN model with neutrino <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ν</mi><mi>e</mi></msub><mo>↔</mo><msub><mi>ν</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> oscillations, we analyze the change in the cosmological constraints in case lepton asymmetry L is big enough to suppress oscillations. We obtain constraints on the lepton asymmetry L. We discuss a possible solution to the dark radiation problem in degenerate BBN models with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ν</mi><mi>e</mi></msub><mo>↔</mo><msub><mi>ν</mi><mi>s</mi></msub></mrow></semantics></math></inline-formula> oscillations in case L is large enough to suppress neutrino oscillations during the BBN epoch. Interestingly, the required value of L for solving the DR problem is close to the value of L indicated by the EMPRESS experiment, and also it is close to the value of lepton asymmetry that is necessary to relax Hubble tension.
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