Constraints on Variation of the Weak Scale from Big Bang Nucleosynthesis

Recently, the EMPRESS collaboration has included new data in the extraction of the primordial $^4$He abundance from Big Bang Nucleosynthesis (BBN), resulting in a determination that differs from the previous value and from theoretical expectations. There have been several studies attempting to explain this anomaly which involve variation of fundamental constants between the time of BBN and the present. Since the Higgs vacuum expectation value (vev) is the only dimensionful parameter in the Standard Model and it is already known to vary during the electroweak phase transition, we consider the possibility that the vev is slightly different during BBN compared to its present value. A modification of the vev changes not only particle masses but also affects, through mass thresholds, the QCD confinement scale. We use the recently developed PRyMordial program to study this variation and its impact on the $^4$He and deuterium abundances. We find that bounds on $|{\delta v}/{v}|$ are approximately $0.01$, and that the EMPRESS result can be explained within $2\sigma$ if $0.008 < {\delta v}/{v}< 0.02$, but at the cost of worsening the current $2\sigma$ discrepancy in the deuterium abundance to over $3\sigma$.