Higgs portal valleys, stability and inflation

TL;DR

This paper investigates the stability of the Higgs potential during inflation, examining how scalar fields coupled via the Higgs portal can or cannot stabilize it, and explores implications for inflationary models and gravitational wave predictions.

Contribution

It demonstrates that minimal Higgs portal models cannot stabilize the potential during inflation if the scalar mass exceeds the instability scale, and clarifies stability conditions independent of inflation.

Findings

Minimal Higgs portal scalars do not stabilize the potential during inflation.

Stable potentials allow inflation along a Mexican hat valley.

False vacuum inflation predicts excessive primordial gravitational waves.

Abstract

The measured values of the Higgs and top quark masses imply that the Standard Model potential is very likely to be unstable at large Higgs values. This is particularly problematic during inflation, which sources large perturbations of the Higgs. The instability could be cured by a threshold effect induced by a scalar with a large vacuum expectation value and directly connected to the Standard Model through a Higgs portal coupling. However, we find that in a minimal model in which the scalar generates inflation, this mechanism does not stabilize the potential because the mass required for inflation is beyond the instability scale. This conclusion does not change if the Higgs has a direct weak coupling to the scalar curvature. On the other hand, if the potential is absolutely stable, successful inflation in agreement with current CMB data can occur along a valley of the potential with a Mexican hat profile. We revisit the stability conditions, independently of inflation, and clarify that the threshold effect cannot work if the Higgs portal coupling is too small. We also show that inflation in a false Higgs vacuum appearing radiatively for a tuned ratio of the Higgs and top masses leads to an amplitude of primordial gravitational waves that is far too high, ruling out this possibility.