BBN bounds on active-sterile neutrino mixing

Abstract

Nucleosynthesis restrictions on mixing of active neutrinos with possible sterile ones are obtained with the account of experimentally determined mixing between all active neutrinos. The earlier derived bounds, valid in the absence of active-active mixing, are reanalyzed and significant difference is found in the resonance case. The results are obtained both analytically and numerically by solution of complete system of integro-differential kinetic equations. A good agreement between analytical and numerical approaches is demonstrated. A role of possibly large cosmological lepton asymmetry is discussed.

Figures (10)

• Figure 1: Numerical results for $\nu_\mu-\nu_s$ mixing. Non resonance case. First panel: Iso-countour lines for $\nu_e$ energy density. Each line corresponds to fixed value of $\nu_e$ energy density. The indicated values are normalized to equilibrium value. Second panel: Iso-contour lines for $\nu_s$ energy density. Third panel: Iso-contour lines for total neutrino contribution to the energy density. Each line corresponds to a fixed value of the number of extra neutrino flavors $\Delta N_{\nu}$. Fourth panel: Total effect of neutrino oscillation on BBN. Each line corresponds to a fixed value of the effective number of neutrinos $\Delta N_{\nu}^{\rm BBN}$ species calculated according to eq. (\ref{['dnbbn']}). Experimental bounds on $\Delta N_{\nu}^{\rm BBN}$ exclude the region above the corresponding curve. Red dotted lines correspond to analytical estimates obtained from eq. (\ref{['dmmuss2']}) and following discussion. The quantities presented in this and in the following figures are taken at the BBN "time", $x_{\rm BBN}=1.4$.
• Figure 2: Numerical results for $\nu_e-\nu_s$ mixing, non resonance case. See Fig.1 for detailed explanation of the various panels and for a definition of the various lines. Red dotted lines correspond to analytical estimates obtained from eq.(\ref{['dmess2']}) and following discussion.
• Figure 3: Comparison between numerical results (solid lines) and analytic estimates (red dotted lines) for $\nu_e-\nu_s$ mixing, resonance case. The various lines show the energy density of sterile neutrinos (at the time of BBN) as a function of the mixing angle $\sin^{2}(2\theta)$, for selected values of the mass difference ${\delta m^2}$. Analytic estimates are obtained from eq. (\ref{['LZ-as']}) and following discussion.
• Figure 4: Comparison between numerical results (solid lines) and analytic estimates (dotted lines) for $\nu_e-\nu_s$ mixing, resonance case. The various lines show the energy density of electron neutrinos (at the time of BBN) as a function of the mixing angle $\sin^{2}(2\theta)$, for selected values of the mass difference ${\delta m^2}$. Blue dotted lines, which are obtained from eqs. (\ref{['LZ-aa']}), do not take into account $\nu_e$ post-resonance evolution. Red dotted lines take it into account following eqs.(\ref{['active-res']}, \ref{['active-res-2']}).
• Figure 5: Numerical results for $\nu_\mu-\nu_s$ mixing, resonance case. See Fig.1 for detailed explanation of the various panels and for a definition of the various lines. Red dotted lines correspond to analytical estimates obtained from eq.(\ref{['LZ-as']}) and following discussions.