Spacetime curvature and the Higgs stability during inflation

Abstract

It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of order $H$ in 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 RG running of non-minimal coupling $\xi$, which either stabilizes the potential against fluctuations for $\xi_{\rm EW} \gtrsim 6\cdot 10^{-2}$, or destabilizes it for $\xi_{\rm EW} \lesssim 2 \cdot 10^{-2}$ when the generated curvature mass is negative. Only in the narrow intermediate region the effect of the curvature mass may be significantly smaller.