We extend a recently developed big bang nucleosynthesis (BBN) code, 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 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 $\mathrm{\Delta }\alpha /\alpha =2\pm 51\mathrm{ppm}$ (parts per million), while for the variation of Newton’s constant the analogous constraint is $\mathrm{\Delta }\alpha /\alpha =2\pm 22\mathrm{ppm}$. We also show that, given these constraints, these models do not provide a solution to the cosmological lithium problem.

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• Big bang nucleosynthesis
• Cosmology
• Grand unified models
• Particle astrophysics