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Recently, the EMPRESS Collaboration has included new data in the extraction of the primordial ${}^4\mathrm{He}$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 yordial program to study this variation and its impact on the ${}^4\mathrm{He}$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 $3\sigma$. Published by the American Physical Society2024 

This review considers models with extended Higgs sectors in which there are tree-level flavor-changing neutral currents (FCNC) mediated by scalars. After briefly reviewing models without tree-level FCNC, several models with such currents are discussed. A popular mass-matrix ansatz, in which the flavor-changing couplings are the geometric mean of the individual flavor couplings, is presented. While it provided a target for experimentalists for three decades, it is now being severely challenged by experiments. Couplings expected to be of [Formula: see text] must be substantially smaller and the ansatz is now not favored. The minimal flavor violation hypothesis is introduced. Then specific models are presented, including the Branco–Grimus–Lavoura models. These models are not yet excluded experimentally, but they are highly predictive and will be tested once heavy Higgs bosons are discovered. We then turn to flavorful models and flavor-changing decays of heavy Higgs bosons, and it is shown that in many of these models, the heavy Higgs could predominantly decay in a flavor-changing manner (such as [Formula: see text] or [Formula: see text]) and experimentalists are encouraged to include these possibilities in their searches.