Primordial nucleosynthesis (or BBN) is one of the three observational evidences for the Big-Bang model. There is indeed a good overall agreement between primordial abundances of D, 3He, 4He and 7Li either deduced from observation or primordial nucleosynthesis calculations. However, there remains a tantalizing discrepancy of a factor of 3-5 between the primordial 7Li abundances either calculated or deduced from observations. Solutions to this problem have been proposed, involving non standard models of the Big-Bang or stellar physics, but first, possible nuclear physics solutions have to be investigated. I will discuss the following topics.
Nuclear reactions, candidates for the destruction of 7Be/7Li, have been proposed
and nuclear physics experiments have been (or are being) conducted to determine their cross-sections.
Particle physics solutions for reducing the 7Li abundance include free thermal neutron injection during BBN, via decays or annihilations of dark matter particles.
CNO production in BBN could affect the evolution of the very first stars but its calculation relies on hundreds of thermonuclear reaction rates including many for which very little experimental data is available. We extended our network to >400 reacions and pointed out the few uncertain reaction rates that can have a significant impact on BBN CNO production .
Testing the constancy of fundamental constants one actually performs a test of General Relativity, that can be extended on astrophysical and cosmological scales. In this context, we explore ways to reduce 7Li production [3,4] and bridge the "A=8 gap" and produce excess CNO .
 D. V'asquez, A. Belikov, A. Coc, J. Silk and E. Vangioni, submitted.
 A. Coc, S. Goriely, Y. Xu, M. Saimpert and E. Vangioni, Astrophys. J., 744 (2012) 158.
 A. Coc, N. Nunes, K. Olive, J.-P. Uzan and E. Vangioni, Phys. Rev. D76 (2007) 023511.
 A. Coc, P. Descouvemont, K. Olive, J.-P. Uzan and E. Vangioni, in preparation.