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Electroweak Vacuum Stability in light of BICEP2

We consider the effect of a period of inflation with a high energy density upon the stability of the Higgs potential in the early universe. The recent measurement of a large tensor-to-scalar ratio, $r_T \sim 0.16$, by the BICEP-2 experiment possibly implies that the energy density during inflation was very high, comparable with the GUT scale. Given that the standard model Higgs potential is known to develop an instability at $Λ\sim 10^{10}$ GeV this means that the resulting large quantum fluctuations of the Higgs field could destabilize the vacuum during inflation, even if the Higgs field starts at zero expectation value. We estimate the probability of such a catastrophic destabilisation given such an inflationary scenario and calculate that for a Higgs mass of $m_h=125.5$ GeV that the top mass must be less than $m_t\sim 172$ GeV. We present two possible cures: a direct coupling between the Higgs and the inflaton and a non-zero temperature from dissipation during inflation.