The accurate evaluation of the nuclear reaction rates and corresponding uncertainties is an essential requisite for a precise determination of light nuclide primordial abundances. The recent measurement of the D(p,gamma)3He radiative capture cross section by the LUNA collaboration, with its order 3% error, represents an important step in improving the theoretical prediction for Deuterium produced in the early universe. In view of this recent result, we present in this paper a full analysis of its abundance, which includes a new critical study of the impact of the other two main processes for Deuterium burning, namely the deuteron-deuteron transfer reactions, D(d,p)3H and D(d,n)3He. In particular, emphasis is given to the statistical method of analysis of experimental data, to a quantitative study of the theoretical uncertainties, and a comparison with similar studies presented in the recent literature. We then discuss the impact of our study on the concordance of the primordial nucleosynthesis stage with the Planck experiment results on the baryon density Omegab h2 and the effective number of neutrino parameter Neff, as function of the assumed value of the 4He mass fraction Yp. While after the LUNA results, the value of Deuterium is quite precisely fixed, and points to a value of the baryon density in excellent agreement with the Planck result, a combined analysis also including Helium leads to two possible scenarios with different predictions for Omegab h2 and Neff. We argue that new experimental results on the systematics and the determination of Yp would be of great importance in assessing the overall concordance of the standard cosmological model.
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