Improved Constraints on the Variation of the Weak Scale from Big Bang Nucleosynthesis

We present an improved calculation of the light element abundances in the framework of Big Bang nucleosynthesis as a function of the Higgs vacuum expectation value $v$. We compare the methods of our calculation to previous literature including the recently published work of Burns et al. [1]. The PDG result for the $^4$He abundance can be explained within $2\sigma$ by $-0.014 \leq \delta v / v \leq 0.026$, for deuterium we find the constraint $-0.005 \leq \delta v / v \leq -0.001$. These bounds are more stringent than what was found earlier.