On stability of the electroweak vacuum and the Higgs portal

In the Standard Model (SM), the Higgs mass around 125 GeV implies that the electroweak vacuum is metastable since the quartic Higgs coupling turns negative at high energies. I point out that a tiny mixing of the Higgs with a heavy singlet can make the electroweak vacuum completely stable. This is due to a tree level correction to the Higgs mass-coupling relation, which survives in the zero-mixing/heavy-singlet limit. Such a situation is experimentally indistinguishable from the SM, unless the Higgs self-coupling can be measured. As a result, Higgs inflation and its variants can still be viable.