A Casimir turning point as the beginning of a small flat universe
Abstract
We study a flat three-torus universe whose contraction is turned around by the negative Casimir energy of Standard Model fields. The trace anomaly forbids conformal matter alone to turn an anisotropic universe around, so matter with w<1/3, most cheaply a positive potential, must supply the negative trace; with antiperiodic fermions the Standard Model supplies the negative energy, and the universe turns at an edge of 722 reduced Planck lengths. The turning point can hold only about five quanta of the lowest modes, whereas a reheating coupling in a time-symmetric past would produce radiation exceeding the Casimir energy by at least 1094, so we read the turn as a beginning rather than a bounce. Negative Casimir energy cannot hold the shape of the torus: its shape state can be real at most once, and for a real Gaussian state survival of the shape on both branches with 90% probability requires that moment to lie within $0.35$ Hubble times of the turn. The natural state, real at the turn, freezes the torus into a nearly rectangular box whose sides typically differ by $16−−18\%$. The microwave background can read this fossil only if the shortest cycle lies between $0.985$ and about $1.04$ last-scattering diameters. At the turn the Higgs quartic coupling is negative, yet zero-point fluctuations of the gauge zero modes keep the Higgs zero mode near the origin with probability above one half for a top-quark pole mass below $172.96$ GeV, given a curvature coupling ξH≳0.08; a pole mass above $173.7$ GeV, within reach of FCC-ee, would exclude this beginning.
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BibTeX
@misc{zhang2026casimir,
title = {{A Casimir turning point as the beginning of a small flat universe}},
author = {Alan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24905},
eprint = {2610.24905},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24905},
}
RIS
TY - UNPB
TI - A Casimir turning point as the beginning of a small flat universe
AU - Alan Zhang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.24905
UR - https://arxiv.org/abs/2610.24905
AB - We study a flat three-torus universe whose contraction is turned around by the negative Casimir energy of Standard Model fields. The trace anomaly forbids conformal matter alone to turn an anisotropic universe around, so matter with w<1/3, most cheaply a positive potential, must supply the negative trace; with antiperiodic fermions the Standard Model supplies the negative energy, and the universe turns at an edge of 722 reduced Planck lengths. The turning point can hold only about five quanta of the lowest modes, whereas a reheating coupling in a time-symmetric past would produce radiation exceeding the Casimir energy by at least 10^94, so we read the turn as a beginning rather than a bounce. Negative Casimir energy cannot hold the shape of the torus: its shape state can be real at most once, and for a real Gaussian state survival of the shape on both branches with 90% probability requires that moment to lie within $0.35$ Hubble times of the turn. The natural state, real at the turn, freezes the torus into a nearly rectangular box whose sides typically differ by $16−−18\%$. The microwave background can read this fossil only if the shortest cycle lies between $0.985$ and about $1.04$ last-scattering diameters. At the turn the Higgs quartic coupling is negative, yet zero-point fluctuations of the gauge zero modes keep the Higgs zero mode near the origin with probability above one half for a top-quark pole mass below $172.96$ GeV, given a curvature coupling ξ_H≳0.08; a pole mass above $173.7$ GeV, within reach of FCC-ee, would exclude this beginning.
ER -