Variation of the Fermi constant and primordial nucleosynthesis

Motivated by the dependence of the fundamental constants on the size of compact dimensions, Kolb, Perry, and Walker considered the effects on primordial nucleosynthesis of variations in some of these constants, including the Fermi constant $G_F$. We note that, in the standard model, a variation in $G_F$ will necessarily imply a variation in the vacuum expectation value of a Higgs field, which in turn will affect the electron mass, quark masses (and thus the neutron-proton mass difference), and the pion mass (and thus the binding energy of the deuteron). We calculate the effect on primordial nucleosynthesis of a variation in the vacuum expectation value of the Higgs field, including all of these factors.