  We constrain the possible time variation of the Higgs vacuum expectation
value ($v$) by recent results on the primordial $^4He$ abundance ($Y_P$). For
that, we use an analytic approach which enables us to take important issues
into consideration, that have been ignored by previous works, like the
$v$-dependence of the relevant cross sections of deuterium production and
photodisintegration, including the full Klein- Nishina cross section.
Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration
of neutrons and protons and incorporate the latest results on the neutron
decay. Finally, we approximate the key-parameters of the primordial $^4He$
production (the mean lifetime of the free neutron and the binding energy of the
deuteron) by terms of $v\over v_0$ (where $v_0$ denotes the present theoretical
estimate). Eventually, we derive the relation $Y_P \simeq 0.2479 - 5.54
(\frac{v-v_0}{v_0})^2 - 0.808~ (\frac{v-v_0}{v_0})$ and the most stringent
limit on a possible time variation of $v$ is given by: $-5.4 \cdot 10^{-4} \leq
\frac{v-v_0}{v_0} \leq 4.4 \cdot 10^{-4}$.

Astrophysics