Probable or Improbable Universe? Correlating Electroweak Vacuum Instability with the Scale of Inflation

TL;DR

This paper investigates how the instability of the Higgs potential during inflation affects the universe's fate, analyzing different evolution scenarios and the impact of Planck-scale corrections on vacuum stability.

Contribution

It provides a comprehensive analysis of Higgs vacuum stability during inflation, considering both tunneling and stochastic effects, and explores the influence of Planck-suppressed operators.

Findings

Vacuum instability depends on inflation scale and post-inflation evolution.

Longer inflation can help avoid catastrophic vacuum decay.

Planck-scale corrections can stabilize the Higgs potential during inflation.

Abstract

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around $\Lambda_I \sim 10^{11}$ GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than $\Lambda_I$ (as preferred by the recent BICEP2 measurement). We perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale of inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation.