From primordial $^4$He abundance to the Higgs field

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 o…