We study primordial nucleosynthesis abundance yields for assumed ranges of cosmological lepton numbers, sterile neutrino mass-squared differences and active-sterile vacuum mixing angles. We fix the baryon-to-photon ratio at the value derived from the cosmic microwave background (CMB) data and then calculate the deviation of the 2H, 4He, and 7Li abundance yields from those expected in the zero lepton number(s), no-new-neutrino-physics case. We conclude that high precision (< 5% error) measurements of the primordial 2H abundance from, e.g., QSO absorption line observations coupled with high precision (< 1% error) baryon density measurements from the CMB could have the power to either: (1) reveal or rule out the existence of a light sterile neutrino if the sign of the cosmological lepton number is known; or (2) place strong constraints on lepton numbers, sterile neutrino mixing properties and resonance sweep physics. Similar conclusions would hold if the primordial 4He abundance could be determined to better than 10%.
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