Higgs instability and de Sitter radiation
  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. 
Gaurav Goswami and Subhendra Mohanty
hep-ph astro-ph.CO hep-th