Electroweak Vacuum (In)Stability in an Inflationary Universe

TL;DR

The paper analyzes electroweak vacuum stability in an inflationary (de Sitter) universe, showing that Hawking-Moss transitions can render the Standard Model Higgs vacuum short-lived during inflation unless the Hubble rate satisfies $H_{ m inf}\lesssim 10^9-10^{12}$ GeV. It also considers inflaton–Higgs interactions that raise the potential curvature, in which case Coleman-de Luccia transitions can dominate and similarly destabilize the vacuum. The work connects vacuum stability to observable tensor modes in the CMB, arguing that Planck-scale tensor detections would indicate new physics stabilizing the EW vacuum, while negligible tensors point to low-scale inflation or curvaton-like perturbations. Overall, the results tightly couple early-un universe dynamics to Higgs sector stability, with Planck tensor measurements providing a potential indirect probe of beyond-Standard-Model stabilization mechanisms.

Abstract

Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: $H_{\rm inf}\lesssim 10^9-10^{12}$ GeV. Models of inflation with such a low rate typically predict negligible tensor perturbations in the cosmic microwave background radiation (CMBR). This is also true for models in which the perturbations are produced by a curvaton field. We also find that if the effective curvature of the Higgs potential at a local maximum (which may be induced by inflaton-Higgs interactions) is large enough, then the decay of the electroweak vacuum is dominated by the Coleman-de Luccia transition. The electroweak vacuum is also short-lived in this case, due to a negative effective self-interaction coupling. Based on our analysis of Higgs vacuum stability during inflation, we conclude that the observation of tensor perturbations by the Planck satellite would provide strong indirect evidence for new physics beyond the Standard Model responsible for stabilisation of the electroweak vacuum.

Figures (1)

• Figure 1: The Higgs potential. For large values of the Higgs field h, the electroweak vacuum configuration is regarded as trivial, $v_{EW}\approx 0$.