Precision prediction for the big-bang abundance of primordial 4He

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 be 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=5x10-10)=0.2462±0.0004 (expt)±<0.0002 (theory). Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, ΩBh2=0.019±0.001, leads to the prediction YP=0.2464±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. copyright 1999 The American Physical Society