  We constrain the possible time variation of the Higgs vacuum expectation
value ($v$) by recent results on the primordial $^4$He abundance ($Y_P$). For
that, we improve the analytic models of the key-processes in our previous
analytic calculation of the primordial $^4$He abundance. Furthermore, the
latest results on the neutron decay, the baryon to photon ratio based on 5-year
WMAP observations and a new dependence of the deuteron binding energy on $v$
are incorporated.
  Finally, we approximate the weak freeze-out, the cross section of
photo-disintegration of the deuteron, the mean lifetime of the free neutron,
the mass difference of neutron and proton, the Fermi coupling constant, the
mass of the electron and the binding energy of the deuteron by terms of $v$, to
constrain its possible time variation by recent results on the primordial
$^4$He abundance: $|\frac{\Delta v}{v}| ~ \leq 1.5 \cdot 10^{-4}$.
