Variation of fundamental constants and the role of A=5 and A=8 nuclei on primordial nucleosynthesis

We investigate the effect of a variation of fundamental constants on primordial element production in big bang nucleosynthesis (BBN). We focus on the effect of a possible change in the nucleon-nucleon interaction on nuclear reaction rates involving the A=5 (Li5 and He5) and A=8 (Be8) unstable nuclei. The reaction rates for He3(d,p)He4 and H3(d,n)He4 are dominated by the properties of broad analog resonances in He5 and Li5 compound nuclei, respectively. While the triple alpha process He4(αα,γ)C12 is normally not effective in BBN, its rate is very sensitive to the position of the "Hoyle state" and could in principle be drastically affected if Be8 were stable during BBN. The nuclear properties (resonance energies in He5 and Li5 nuclei, and the binding energies of Be8 and D) are all computed in a consistent way using a microscopic cluster model. The n(p,γ)d, He3(d,p)He4, H3(d,n)He4, and He4(αα,γ)C12 reaction rates are subsequently calculated as a function of the nucleon-nucleon interaction that can be related to the fundamental constants. We found that the effect of the variation of constants on the He3(d,p)He4, H3(d,n)He4, and He4(αα, γ)C12 reaction rates is not sufficient to induce a significant effect on BBN, even if Be8 was stable. In particular, no significant production of carbon by the triple alpha reaction is found when compared to standard BBN. Finally, we complement our earlier work on the effect of coupled variation of fundamental constants inducing variations of the binding energy of deuterium, the Fermi constant, and the neutron-proton mass difference, that affect the weak rates and the n(p,γ)d, A=2 bottleneck reaction.