The cosmological Higgstory of the vacuum instability

TL;DR

This paper investigates the cosmological implications of the Higgs potential instability, deriving bounds on inflationary parameters and linking Higgs stability to quantum gravity, with results consistent with observed particle masses.

Contribution

It clarifies gauge dependence issues and explores the cosmological evolution of the Higgs field, providing new bounds on inflation and a novel connection to quantum gravity.

Findings

Anti-de Sitter patches are lethal for the universe.

Upper bounds on the Hubble constant during inflation.

Predictions for Higgs and top masses consistent with measurements.

Abstract

The Standard Model Higgs potential becomes unstable at large field values. After clarifying the issue of gauge dependence of the effective potential, we study the cosmological evolution of the Higgs field in presence of this instability throughout inflation, reheating and the present epoch. We conclude that anti-de Sitter patches in which the Higgs field lies at its true vacuum are lethal for our universe. From this result, we derive upper bounds on the Hubble constant during inflation, which depend on the reheating temperature and on the Higgs coupling to the scalar curvature or to the inflaton. Finally we study how a speculative link between Higgs meta-stability and consistence of quantum gravity leads to a sharp prediction for the Higgs and top masses, which is consistent with measured values.