Gauge Field Fluctuations Protect the Higgs Vacuum When a Small Universe Begins

The Standard Model Higgs quartic coupling $λ$ turns negative at high energies. We show that in a small periodic box with antiperiodic fermions, zero-point fluctuations of the constant gauge modes turn the Higgs zero mode into a resonance for $λ<0$, whose width falls exponentially in $|λ|^{-1/2}$. A