Precision prediction for the big-bang abundance of primordial4He

Abstract

Within the standard models of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of 4 He to a theoretical uncertainty of less than 0.1 % (δY P < ±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, τ n = 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 4 He abundance are presented in the form of an accurate fitting formula. Summarizing our work in one number, Y P (η = 5 × 10 −10 ) = 0.2462 ± 0.0004 (expt) ± < 0.0002 (theory). Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance, Ω B h 2 = 0.019 ± 0.001, leads to the prediction: Y P = 0.2464 ± 0.0005 (D/H) ± < 0.0002 (theory) ± 0.0005 (expt). This "prediction" and an accurate measurement of the primeval 4 He abundance will allow an important consistency test of primordial nucleosynthesis.

Estimating reaction rates and uncertainties for primordial nucleosynthesis

“…On the other, the errors in 4 He, especially at higher values of Ω B , are dominated by the uncertainty in the weak coupling constant and by uncertainties in calculating the matrix elements for the weak processes. These errors and theoretical uncertainties have been analyzed exhaustively by Lopez and Turner [24], and we FIG. 13.…”

“…The 4 He uncertainty comes from Ref. [24]. Boxes indicate 95% cl abundances from observation [87][88][89].…”

“…This is also the only process 4 He yields are sensitive to at likely values of baryon density. Lopez and Turner [24] have incorporated in a coherent and consistent way a number of small but important physics and numerical corrections to the weak rates, and we take yields for this nuclide from their work. Second, there was not enough data coverage to use our technique for proton-neutron capture, p(n, γ)d, so we used a theoretical model of this process as described in Sec.…”

Neutrino energy transport in weak decoupling and big bang nucleosynthesis

“…The feedback between neutrino energy transport and plasma conditions is especially sensitive to electron-positron pair number density as these are key targets for neutrino scattering. Previous works [1,2,10,44] include the effects of finite temperature QED radiative corrections. The corrections have been calculated for the electron mass and wave function renormalization, the electron-photon vertex and infrared photon emission and absorption.…”

“…The work we describe here builds on the many previous studies of the evolution of the neutrino energy distribution functions in the early universe (see Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and Appendix A). Higher precision in theoretical calculations of neutrino transport and nucleosynthesis in the early universe is warranted by recent and anticipated improvement in the precision of cosmological observations.…”