Abstract
Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around Λ I ∼ 1011 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 Λ 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.
Highlights
The question of the evolution of the Higgs field during inflation has become important in light of the recent BICEP2 [8] measurement of the tensor-scalar ratio, r, which directly probes the scale of inflation, H2 = πMP2 ∆2Rr, 16
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 have studied the evolution of the Higgs field during inflation in the presence of a potentially catastrophic true minimum
Summary
We describe the formalism for studying the evolution of the Higgs field during inflation. We begin with a single Hubble patch, assuming h = 0 initially, and follow the Higgs field evolution as this region inflates. For large Higgs field values h v, where v = 246 GeV is the Higgs vev in the electroweak vacuum, we make use of the potential. Since λeff runs negative at higher scales, the Higgs potential turns over at some scale Λmax. Our goal is to explore the Higgs evolution in and elucidate the phenomenological relevance of these regimes. For simplicity and ease of comparison with earlier studies, we first concentrate on the Higgs potential without any corrections from higher dimension operators; in section 4, we will consider Planck-suppressed corrections to the Higgs potential, which can be significant. We assume that H is (to a very good approximation) constant during inflation, in order to study the general phenomenon of electroweak vacuum stability during inflation in a model-independent manner
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