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

Abstract

The Standard Model Higgs quartic coupling $\lambda$ 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 $\lambda <0$, whose width falls exponentially in $|\lambda {|}^{-1/2}$. A box lasting $N$ light-crossing times keeps its vacuum with probability above $1/2$ for $\lambda >{\lambda }_c(N)$, which depends on $N$ only logarithmically. For a universe that begins at a Casimir turning point, ${\lambda }_c\approx -0.012$ lies below the Standard Model value $-0.0098$; given a curvature coupling ${\xi }_H\gtrsim 0.08$, survival has probability above $1/2$ for $m_t<172.96$ GeV and $\approx 0.7$ for current data, and FCC-ee can exclude this beginning if $m_t\gtrsim 173.7$ GeV.

arXiv comment8 pages, 3 figures, 1 table, including End Matter. Supplemental Material (code and data of the static-box and abelian-Higgs calculations) in the ancillary files. Companion paper: arXiv:2610.24905. Code and data: https://doi.org/10.5281/zenodo.23434068 and technical report: https://doi.org/10.5281/zenodo.23434140