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arXiv · 1404.5953

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

Anson Hook·John Kearney·Bibhushan Shakya·Kathryn M. Zurek
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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.

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Anson Hook, John Kearney, Bibhushan Shakya, Kathryn M. Zurek. 2014-04-23. Probable or Improbable Universe? Correlating Electroweak Vacuum Instability with the Scale of Inflation. https://doi.org/10.1007/jhep01(2015)061

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