Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. Standard BBN is now a parameter free theory, since the baryonic density of the Universe has been deduced with an unprecedented precision from observations of the anisotropies of the cosmic microwave background (CMB) radiation. There is a good agreement between the primordial abundances of 4He, D, 3He and 7Li deduced from observations and from primordial nucleosynthesis calculations. However, the 7Li calculated abundance is significantly higher than the one deduced from spectroscopic observations and remains an open problem. In addition, recent deuterium observations have drastically reduced the uncertainty on D/H, to reach a value of 1.6%. It needs to be matched by BBN predictions whose precision is now limited by thermonuclear reaction rate uncertainties. This is especially important as many attempts to reconcile Li observations with models lead to an increased D prediction. Here, we re-evaluates the D(p,g)3He, D(d,n)3He and D(d,p)3H reaction rates that govern deuterium destruction, incorporating new experimental data and carefully accounting for systematic uncertainties. Contrary to previous evaluations, we use theoretical ab initio models for the energy dependence of the S-factors. As a result, these rates increase at BBN temperatures, leading to a reduced value of D/H = (2.45$pm0.10)times10^{-5}$ (2$sigma$), in agreement with observations.
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