We study Coleman-De Luccia tunneling of the Standard Model Higgs field duringinflation in the case when the electroweak vacuum is metastable. We verify thatthe tunneling rate is exponentially suppressed. The main contribution to thesuppression is the same as in flat space-time. We analytically estimate thecorrections due to the expansion of the universe and an effective mass term inthe Higgs potential that can be present at inflation.
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