Precision Prediction for the Big - Bang Abundance of Primordial 4 He

Within the standard models of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of 4He to a theoretical uncertainty of less than 0.1% (δYP < ±0.0002), improving the current theoretical precision by a factor of 10. At this accuracy the uncertainty in the abundance is dominated by the experimental uncertainty in the neutron mean lifetime, τn = 885.4±2.0 sec. The following physical effects were included in the calculation: the zero and finite-temperature radiative, Coulomb and finite-nucleon-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 designed to control numerical errors to less than 0.1%. Our predictions for the 4He abundance are presented in the form of an accurate fitting formula. Summarizing our work in one number, YP (η = 5 × 10−10) = 0.2460 ± 0.0004 (expt) ± < 0.0002 (theory). Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, ΩB h 2 = 0.019± 0.001, leads to the prediction: YP = 0.2462± 0.0005 (D/H)± < 0.0002 (theory) ± 0.0005 (expt). This “prediction” and an accurate measurement of the primeval 4He abundance will allow an important consistency test of primordial nucleosynthesis in the early universe.