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

TL;DR

This paper discusses how quantum fluctuations of the Higgs field during cosmic inflation could lead to vacuum instability, emphasizing the importance of extreme-value statistics in assessing the risk of catastrophic regions forming.

Contribution

It introduces the use of extreme-value statistics to better estimate the probability of Higgs vacuum instability during inflation, refining previous bounds on the Hubble rate.

Findings

Extreme-value statistics provide a more accurate bound on inflationary Hubble rate.

The new bound is about a factor of √2 stronger than previous estimates.

The approach offers a qualitatively distinct perspective on Higgs vacuum stability during inflation.

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.