Spacetime curvature and the Higgs stability during inflation

TL;DR

This paper investigates how spacetime curvature during high-scale inflation influences the stability of the Higgs field, showing that curvature effects can either stabilize or destabilize the electroweak vacuum depending on the non-minimal coupling parameter.

Contribution

It provides a detailed calculation of the Higgs effective potential including curvature corrections, revealing the role of RG running of the non-minimal coupling in vacuum stability during inflation.

Findings

High inflationary scale generates a large curvature mass affecting Higgs stability.

Stability is achieved for non-minimal coupling   6^{-2}  0.06.

Destabilization occurs for   2^{-2}  0.02, with a narrow intermediate region.

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.