Limits on Active-Sterile Neutrino Mixing and the Primordial Deuterium Abundance

Studies of limits on active-sterile neutrino mixing derived from big bang nucleosynthesis considerations are extended to consider the dependance of these constraints on the primordial deuterium abundance. This study is motivated by recent measurements of D/H in quasar absorption systems, which at present yield discordant results. Limits on active-sterile mixing are somewhat relaxed for high D/H. For low D/H ($\approx 2 \times 10^{-5}$), no active-sterile neutrino mixing is allowed by currently popular upper limits on the primordial $^4$He abundance $Y$. For such low primordial D/H values, the observational inference of active-sterile neutrino mixing by upcoming solar neutrino experiments would imply that $Y$ has been systematically underestimated, unless there is new physics not included in standard BBN.