Spacetime Dynamics of a Higgs Vacuum Instability During Inflation

Abstract

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.

36 pages, 11 figures; revised to match published version

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• Electroweak Vacuum Metastability and Low-scale Inflation
• Do metric fluctuations affect the Higgs dynamics during inflation?
• Cosmological stochastic Higgs stabilization