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Standard Model Higgs Peaks: a Note on the Vacuum Instability during Inflation

G. Franciolini, A. Kehagias, A. Riotto

TL;DR

The paper investigates the Standard Model Higgs vacuum stability during cosmic inflation, where large quantum fluctuations could push the Higgs over the instability barrier and form AdS patches. It advocates extreme-value statistics for the maximum Higgs excursion across ${\cal N}=e^{3N}$ Hubble patches, deriving a most probable peak $\hat{h}$ and a tail-bound that yields a tighter constraint on the inflationary Hubble rate, $\frac{H}{h_{\max}} \approx \frac{\pi}{\sqrt{3}\,N} \sim 0.03$, compared to the conventional bound. The authors show the maximum distribution follows a double-exponential form and discuss alternative regimes (Hawking-Moss, curvature coupling) with subleading maxima remaining negligible. This work highlights that rare peak events, rather than averages, govern cosmological vacuum stability and provides a qualitatively distinct, tail-driven criterion for inflationary models.

Abstract

In the Standard Model, the Higgs potential develops an instability at high field values when the quartic self-coupling runs negative. Large quantum fluctuations during cosmic inflation could drive the Higgs field beyond the potential barrier, creating regions that would be catastrophic for our observable universe. We point out that the extreme-value statistics describing the peaks (maxima) of the Higgs values is the correct statistics to infer the condition to avoid vacuum instability. Even if this statistics delivers a bound on the Hubble rate during inflation which is only a factor $\sqrt{2}$ stronger than the one commonly adopted in the literature, it is qualitatively distinct and we believe worthwhile communicating it.

Standard Model Higgs Peaks: a Note on the Vacuum Instability during Inflation

TL;DR

The paper investigates the Standard Model Higgs vacuum stability during cosmic inflation, where large quantum fluctuations could push the Higgs over the instability barrier and form AdS patches. It advocates extreme-value statistics for the maximum Higgs excursion across Hubble patches, deriving a most probable peak and a tail-bound that yields a tighter constraint on the inflationary Hubble rate, , compared to the conventional bound. The authors show the maximum distribution follows a double-exponential form and discuss alternative regimes (Hawking-Moss, curvature coupling) with subleading maxima remaining negligible. This work highlights that rare peak events, rather than averages, govern cosmological vacuum stability and provides a qualitatively distinct, tail-driven criterion for inflationary models.

Abstract

In the Standard Model, the Higgs potential develops an instability at high field values when the quartic self-coupling runs negative. Large quantum fluctuations during cosmic inflation could drive the Higgs field beyond the potential barrier, creating regions that would be catastrophic for our observable universe. We point out that the extreme-value statistics describing the peaks (maxima) of the Higgs values is the correct statistics to infer the condition to avoid vacuum instability. Even if this statistics delivers a bound on the Hubble rate during inflation which is only a factor stronger than the one commonly adopted in the literature, it is qualitatively distinct and we believe worthwhile communicating it.
Paper Structure (2 sections, 21 equations, 1 figure)

This paper contains 2 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Higgs peaks and conclusions

Figures (1)

  • Figure 1: The probability distribution for the extreme value of $h$ assuming $N=10^4$ realizations. We compare $10^3$ Monte Carlo realizations and the analytical distribution.