A smooth beginning for spacetime II: How the de Sitter horizon erases the no-boundary catastrophe
- 1None
Abstract
Paper II of the trilogy "A smooth beginning for spacetime." The Feldbrugge–Lehners–Turok theorem — that the Lorentzian no-boundary path integral weights perturbations by an inverse Gaussian, with no rescue by any lapse contour — is taken as a diagnosis. Where subsequent responses kept the surface a = 0 and changed its dressing (Robin conditions at zero size, Robin conditions on the perturbations, momentum specifications, or setting the path integral aside), this paper changes the surface: a = 0 is a branch point of the perturbation equation, not a Cauchy surface, and the geometry retains no boundary when the fluctuation data moves to the de Sitter throat — the one surface where the problem is real and well-posed. There the conjugate saddle pair coalesces and cap regularity provably selects the Bunch–Davies vacuum (11 orders). The state is then dynamically protected: a KMS identity certifies the static-patch bath thermal at exactly H/2π; multipoles relax at (L+1)H; ≥99% of the bias is erased within 1–2 Hubble times; an exact budget theorem identifies the entropy produced with the biased state's relative entropy to Bunch–Davies, collected by the horizon; and the single falsifying configuration (a cross-chirality dark state) is constructed and excluded by O(3) isometry. The record includes the preprint, all figures, and nine self-contained Python verification scripts with logs; every quantitative claim is gated against analytic or independently computed values. Drafting and computation were assisted by a large language model (Claude, Anthropic); the author takes sole responsibility. No specific funding was received.
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BibTeX
@misc{williams2026smooth,
title = {{A smooth beginning for spacetime II: How the de Sitter horizon erases the no-boundary catastrophe}},
author = {James Laurence Williams},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21328146},
url = {https://doi.org/10.5281/zenodo.21328146},
note = {CC BY},
}
RIS
TY - UNPB
TI - A smooth beginning for spacetime II: How the de Sitter horizon erases the no-boundary catastrophe
AU - James Laurence Williams
PY - 2026
DA - 2026/07/12
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21328146
UR - https://doi.org/10.5281/zenodo.21328146
AB - Paper II of the trilogy "A smooth beginning for spacetime." The Feldbrugge–Lehners–Turok theorem — that the Lorentzian no-boundary path integral weights perturbations by an inverse Gaussian, with no rescue by any lapse contour — is taken as a diagnosis. Where subsequent responses kept the surface a = 0 and changed its dressing (Robin conditions at zero size, Robin conditions on the perturbations, momentum specifications, or setting the path integral aside), this paper changes the surface: a = 0 is a branch point of the perturbation equation, not a Cauchy surface, and the geometry retains no boundary when the fluctuation data moves to the de Sitter throat — the one surface where the problem is real and well-posed. There the conjugate saddle pair coalesces and cap regularity provably selects the Bunch–Davies vacuum (11 orders). The state is then dynamically protected: a KMS identity certifies the static-patch bath thermal at exactly H/2π; multipoles relax at (L+1)H; ≥99% of the bias is erased within 1–2 Hubble times; an exact budget theorem identifies the entropy produced with the biased state's relative entropy to Bunch–Davies, collected by the horizon; and the single falsifying configuration (a cross-chirality dark state) is constructed and excluded by O(3) isometry. The record includes the preprint, all figures, and nine self-contained Python verification scripts with logs; every quantitative claim is gated against analytic or independently computed values. Drafting and computation were assisted by a large language model (Claude, Anthropic); the author takes sole responsibility. No specific funding was received.
ER -