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