A remarkable prediction of the Standard Model is that, in the absence of
corrections lifting the energy density, the Higgs potential becomes negative at
large field values. If the Higgs field samples this part of the potential
during inflation, the negative energy density may locally destabilize the
spacetime. We use numerical simulations of the Einstein equations to study the
evolution of inflation-induced Higgs fluctuations as they grow towards the true
(negative-energy) minimum. These simulations show that forming a single patch
of true vacuum in our past light cone during inflation is incompatible with the
existence of our Universe; the boundary of the true vacuum region grows outward
in a causally disconnected manner from the crunching interior, which forms a
black hole. We also find that these black hole horizons may be arbitrarily
elongated---even forming black strings---in violation of the hoop conjecture.
By extending the numerical solution of the Fokker-Planck equation to the
exponentially suppressed tails of the field distribution at large field values,
we derive a rigorous correlation between a future measurement of the
tensor-to-scalar ratio and the scale at which the Higgs potential must receive
stabilizing corrections in order for the Universe to have survived inflation
until today.Comment: 36 pages, 11 figures; revised to match published versio
