  Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be
the Standard Model Higgs boson, the electroweak vacuum would be a metastable
state at 98% C.L. In this paper we argue that, during inflation, the
electroweak vacuum can actually be very short-lived, contrary to the conclusion
that follows from the flat spacetime analysis. Namely, in the case of a pure
Higgs potential the electroweak vacuum decays via the Hawking-Moss transition,
which has no flat spacetime analogue. As a result, the Higgs vacuum is
unstable, unless the rate of inflation is low enough: $H_{\rm inf}\lesssim
10^9-10^{12}$ GeV. Models of inflation with such a low rate typically predict
negligible tensor perturbations in the cosmic microwave background radiation
(CMBR). This is also true for models in which the perturbations are produced by
a curvaton field. We also find that if the effective curvature of the Higgs
potential at a local maximum (which may be induced by inflaton-Higgs
interactions) is large enough, then the decay of the electroweak vacuum is
dominated by the Coleman-de Luccia transition. The electroweak vacuum is also
short-lived in this case, due to a negative effective self-interaction
coupling. Based on our analysis of Higgs vacuum stability during inflation, we
conclude that the observation of tensor perturbations by the Planck satellite
would provide strong indirect evidence for new physics beyond the Standard
Model responsible for stabilisation of the electroweak vacuum.
