Primordial nucleosynthesis and neutrino physics

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%. We have performed new Big Bang Nucleosynthesis calculations which employ arbitrarily-specified, time-dependent neutrino and antineutrino distribution functions for each of up to four neutrino flavors. We self-consistently couple these distributions to the thermodynamics, the expansion rate and scale factor-time/temperature relationship, as well as to all relevant weak, electromagnetic, and strong nuclear reaction processes in the early universe. With this approach, we can treat any scenario in which neutrino or antineutrino spectral distortion might arise. These scenarios might include, for example, decaying particles, active-sterile neutrino oscillations, and active-active neutrino oscillations in the presence of significant lepton numbers. Our calculations allow lepton numbers and sterile neutrinos to be constrained with observationally- determined primordial helium and deuterium abundances. We have modified a standard BBN code to perform these calculations and have made it available to the community. We have applied a fully relativistic Coulomb wave correction to the weak reactions in the full Kawano/ Wagoner Big Bang Nucleosynthesis (BBN) code. We have also added the zero temperature radiative correction. We find that using this higher accuracy Coulomb correction results in good agreement with previous work, giving only a modest ̃ 0.04% increase in helium mass fraction over correction prescriptions applied previously in BBN calculations. We have calculated the effect of these corrections on other light element abundance yields in BBN and we have studied these yields as functions of electron neutrino lepton number. This has allowed insights into the role of the Coulomb correction in the setting of the neutron-to-proton ratio during the BBN epoch. We find that the lepton capture processes' contributions to this ratio are only second order in the Coulomb correction