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 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 ^ { 4 } He 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 ~ { } \left ( \frac { v - v _ { 0 } } { v _ { 0 } } \right ) ^ { 2 } -0.808 ~ { } \left% ( \frac { v - v _ { 0 } } { v _ { 0 } } \right ) 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 } .