Constraints on the variation of the fine structure constant from big bang nucleosynthesis

We put bounds on the variation of the value of the fine structure constant $\alpha$, at the time of big bang nucleosynthesis. We study carefully all light elements up to ${}^7$Li. We correct a previous upper limit on $|\Delta \alpha /\alpha |$ estimated from ${}^4\mathrm{He}$ primordial abundance and we find interesting new potential limits (depending on the value of the baryon-to-photon ratio) from ${}^7\mathrm{Li},$ whose production is governed to a large extent by Coulomb barriers. The presently unclear observational situation concerning the primordial abundances precludes a better limit than $|\Delta \alpha /\alpha |\lesssim 2\times {10}^{-2},$ two orders of magnitude less restrictive than previous bounds. In fact, each of the (mutually exclusive) scenarios of standard big bang nucleosynthesis proposed, one based on a high value of the measured deuterium primordial abundance and one based on a low value, may describe some aspects of data better if a change in $\alpha$ of this magnitude is assumed.