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

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

Robert E. Lopez
(
- Chicago U. and
- Fermilab
)
,
Michael S. Turner
(
- Chicago U. and
- Fermilab and
- Chicago U., EFI
)

Jul, 1998

28 pages

Published in:

Phys.Rev.D 59 (1999) 103502

e-Print:

astro-ph/9807279 [astro-ph]

DOI:

10.1103/PhysRevD.59.103502

Report number:

FERMILAB-PUB-98-232-A

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Abstract: (arXiv)

Within the standard models of particle physics and cosmology we have calculated the big-bang prediction for the primordial abundance of \he to a theoretical uncertainty of less than 0.1 \pct

(\delta Y_P < \pm 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,

\tau_n = 885.4 \pm 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-

\alpha

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\pct. Our predictions for the \EL[4]{He} abundance are presented in the form of an accurate fitting formula. Summarizing our work in one number,

Y_P(\eta = 5\times 10^{-10}) = 0.2462 \pm 0.0004 (expt) \pm < 0.0002 (theory)

. Further, the baryon density inferred from the Burles-Tytler determination of the primordial D abundance,

\Omega_B h^2 = 0.019\pm 0.001

, leads to the prediction:

Y_P = 0.2464 \pm 0.0005 (D/H) \pm < 0.0002 (theory) \pm 0.0005 (expt)

. This ``prediction'' and an accurate measurement of the primeval \he abundance will allow an important consistency test of primordial nucleosynthesis.

cosmological model
light nucleus: production
helium
electron nucleon: interaction
radiative correction: finite temperature
correction: Coulomb
nucleon: mass
mass: correction
plasma: density
electron: mass

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