  If the Standard Model (SM) of elementary particle physics is assumed to hold
good to arbitrarily high energies, then, for the best fit values of the
parameters, the scalar potential of the Standard Model Higgs field turns
negative at a high scale $\mu_{\rm inst}$. If the physics beyond the SM is such
that it does not modify this feature of the Higgs potential and if the Hubble
parameter during inflation ($H_{\rm inf}$) is such that $H_{\rm inf} \gg
\mu_{\rm inst}$, then, quantum fluctuations of the SM Higgs during inflation
make it extremely unlikely that after inflation it will be found in the
metastable vacuum at the weak scale. In this work, we assume that (i) during
inflation, the SM Higgs is in Bunch-Davies vacuum state, and, (ii) the question
about the stability of the effective potential must be answered in the frame of
the freely falling observer (just like in Minkowski spacetime), and then use
the well known fact that the freely falling observer finds Bunch-Davies vacuum
to be in thermal state to show that the probability to end up in the
electroweak vacuum after inflation is reasonably high.
