Helium and Deuterium Abundances as a Test for the Time Variation of the Fine Structure Constant and the Higgs Vacuum Expectation Value

We use the semi-analytic method of \citet{Esma91} to calculate the abundances of Helium and Deuterium produced during Big Bang nucleosynthesis assuming the fine structure constant and the Higgs vacuum expectation value may vary in time. We analyze the dependence on the fundamental constants of the nucleon mass, nuclear binding energies and cross sections involved in the calculation of the abundances. Unlike previous works, we do not assume the chiral limit of QCD. Rather, we take into account the quark masses and consider the one-pion exchange potential, within perturbation theory, for the proton-neutron scattering. However, we do not consider the time variation of the strong interactions scale but attribute the changes in the quark masses to the temporal variation of the Higgs vacuum expectation value. Using the observational data of the helium and deuterium, we put constraints on the variation of the fundamental constants between the time of nucleosynthesis and the present time.