Probing Unification Scenarios with Big Bang Nucleosynthesis

We extend a recently developed Big Bang Nucleosynthesis (BBN) code, {\tt PRyMordial}, to constrain a broad class of Grand Unified Theories to which BBN is sensitive, since these lead to varying fundamental couplings. A previously developed self-consistent perturbative analysis of the effects of these variations has been implemented in {\tt PRyMordial}, leading to robust constraints of the value of the fine-structure constant, $\alpha$, at the BBN epoch using current observations of Helium-4 and Deuterium abundances. We explored two different viable scenarios, relying on alternative assumptions on the gravitational sector: the variation of the gravitational coupling can be implemented by varying either particle masses, or Newton's gravitational constant. For the variation of masses, we obtained at $68\%$ confidence level a constraint on the relative variation of $\alpha$, between the BBN epoch and the present-day laboratory value, of $\Delta\alpha/\alpha=2\pm51$ ppm (parts per million), while for the variation of Newton's constant the analogous constraint is $\Delta\alpha/\alpha=2\pm22$ ppm. We also show that, given these constraints, these models do not provide a solution to the cosmological Lithium problem.