Spacetime Curvature and the Higgs Stability During Inflation

It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of the order H in the case of a high inflationary scale as suggested by BICEP2. We compute the standard model Higgs effective potential including UV-induced curvature corrections at one-loop level. We find that for a high inflationary scale a large curvature mass is generated due to renormalization group running of nonminimal coupling ξ, which either stabilizes the potential against fluctuations for ξEW≳6×10(-2), or destabilizes it for ξEW≲2×10(-2) when the generated curvature mass is negative. Only in the narrow intermediate region may the effect of the curvature mass be significantly smaller.