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

Abstract

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 box lasting $N$ light-crossing times keeps its vacuum with probability above $1/2$ for $λ>λ_c(N)$, which depends on $N$ only logarithmically. For a universe that begins at a Casimir turning point, $λ_c\approx-0.012$ lies below the Standard Model value $-0.0098$; given a curvature coupling $ξ_H\gtrsim0.08$, survival has probability above $1/2$ for $m_t<172.96$ GeV and $\approx0.7$ for current data, and FCC-ee can exclude this beginning if $m_t\gtrsim173.7$ GeV.