An Accurate Calculation of the Big - Bang Prediction for the Abundance of Primordial Helium

Within the standard model of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of Helium to a theoretical uncertainty of 0.1% (δYP = ±0.0002). At this accuracy the uncertainty in the abundance is dominated by the experimental uncertainty in the neutron mean lifetime, τn = 885.3 ± 2.0 sec. The following physical effects were included in the calculation: the zero and finite-temperature radiative, Coulomb and finitenucleon mass corrections to the weak rates; order-α quantum-electrodynamic correction to the plasma density, electron mass, and neutrino temperature; and incomplete neutrino decoupling. New results for the finite-temperature radiative correction and the QED plasma correction were used. In addition, we wrote a new and independent nucleosynthesis code to control numerical errors to less than 0.1%. Our predictions for the 4He abundance are summarized with an accurate fitting formula. Summarizing our work in one number, YP (η = 5× 10−10) = 0.2460 ± 0.0004 (expt) ± < 0.0002 (theory).