Spacetime curvature and the Higgs stability during inflation

TL;DR

The standard model Higgs effective potential is computed including UV-induced curvature corrections at one-loop level and it is found that for a high inflationary scale a large curvature mass is generated due to renormalization group running of nonminimal coupling ξ.

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 $ξ$, which either stabilizes the potential against fluctuations for $ξ_{\rm EW} \gtrsim 6\cdot 10^{-2}$, or destabilizes it for $ξ_{\rm EW} \lesssim 2 \cdot 10^{-2}$ when the generated curvature mass is negative. Only in the narrow intermediate region the effect of the curvature mass may be significantly smaller.

Figures (4)

• Figure 1: RGE running of the SM couplings $g_3$, $y_{\rm t}$, $g$, $g'$, $\lambda$ and the non-minimal gravity coupling $\Xi \equiv (\xi - 1/6 )/(\xi_{\rm EW} - 1/6 )$.
• Figure 2: The Higgs effective potential without (top) and with (bottom) curvature corrections for $H = 10^{10}\;{\rm GeV}$ and $\xi_{\rm EW} = 0.1$. The dashed lines correspond to the approximation (\ref{['Lmax']}-\ref{['Vmax']}) for the maximum.
• Figure 3: The Higgs effective potential including curvature corrections with $H = 10^{10}\;{\rm GeV}$ and $\xi_{\rm EW} = 0$.
• Figure 4: The parametric regions I (blue, top), where $V_{\rm max}^{1/4} \gtrsim H$ and the transition probability to unstable vacuum is suppressed, and II (red, bottom), where the EW vacuum is unstable for all $\phi$ due to large negative curvature mass.