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It has been proposed that an asymmetry in the electron neutrino sector may begenerated by resonant active-sterile neutrino transformations during Big BangNucleosynthesis (BBN). We calculate the change in the primordial $^4$He yield$Y$ resulting from this asymmetry, taking into account both the time evolutionof the $\nu_e$ and $\bar\nu_e$ distribution function and the spectraldistortions in these. We calculate this change in two schemes: (1) a leptonasymmetry directly generated by $\nu_e$ mixing with a lighter right-handedsterile neutrino $\nu_s$; and (2) a lepton asymmetry generated by a$\nu_\tau\leftrightarrow\nu_s$ or $\nu_\mu\leftrightarrow\nu_s$ transformationwhich is subsequently partially converted to an asymmetry in the$\nu_e\bar\nu_e$ sector by a matter-enhanced active-active neutrinotransformation. In the first scheme, we find that the percentage change in $Y$is between -1% and 9% (with the sign depending on the sign of the asymmetry),bounded by the Majorana mass limit $m_{\nu_e}\la 1$ eV. In the second scheme,the maximal percentage reduction in $Y$ is 2%, if the lepton number asymmetryin neutrinos is positive; Otherwise, the percentage increase in $Y$ is $\la 5%$for $m^2_{\nu_\mu,\nu_\tau}-m^2_{\nu_s}\la 10^4$ eV. We conclude that thechange in the primordial $^4$He yield induced by a neutrino-mixing-generatedlepton number asymmetry can be substantial in the upward direction, but limitedin the downward direction.Comment: 15 pages, 7 figures, submitted to PR

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Neutrino-mixing-generated lepton asymmetry and the primordial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:math>abundance

Neutrino-mixing-generated lepton asymmetry and the primordial4Heabundance