  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.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory