Using the semianalytic method proposed by Esmailzadeh and coworkers we calculate the abundances of the light elements produced during primordial nucleosynthesis assuming that the gauge coupling constants of the fundamental interactions may vary. We analyze the dependence of the nucleon masses, nuclear binding energies, and cross sections involved in the calculation of the abundances with the fundamental constants assuming the chiral limit of QCD. We obtain the abundances of light elements as a function of the fundamental constants. Finally, using the observational data of D, 3 He, 4 He, and 7 Li, we estimate constraints on the variation of the fundamental constants between the time of primordial nucleosynthesis and the present. All observational abundances and the WMAP estimate of the baryon density can be fitted to the theoretical predictions with varying coupling constants. The possible systematic errors in the observational data preclude stronger conclusions.

Aims. We calculate the bounds on the variation in the fine structure constant at the time of primordial nucleosynthesis and at the time of neutral hydrogen formation. We used these bounds and other bounds from the late universe to test the Bekenstein model. Methods. We modified the Kawano code, CAMB, and CosmoMC to include the possible variation in the fine structure constant. We used observational primordial abundances of D, 4 He, and 7 Li, recent data from the cosmic microwave background, and the 2dFGRS power spectrum, to obtain bounds on the variation in α. We calculated a piecewise solution to the scalar field equation of the Bekenstein model in two different regimes: i) matter and radiation, ii) matter and cosmological constant. We match both solutions with the appropriate boundary conditions. We performed a statistical analysis, using the bounds obtained from the early universe and other bounds from the late universe to constrain the free parameters of the model. Results. Results are consistent with no variation in α for the early universe. Limits on α are inconsistent with the scale length of the theory l being larger than the Planck scale. Conclusions. In order to fit all observational and experimental data, the assumption l > L p implied in Bekenstein's model has to be relaxed.

We study the time variation of fundamental constants in the early Universe. Using data from primordial light nuclei abundances, CMB and the 2dFGRS power spectrum, we put constraints on the time variation of the fine structure constant α, and the Higgs vacuum expectation value < v > without assuming any theoretical framework. A variation in < v > leads to a variation in the electron mass, among other effects. Along the same line, we study the variation of α and the electron mass me. In a purely phenomenological fashion, we derive a relationship between both variations.

We use the semi-analytic method of Esmailzadeh et al. (1991) 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.