Comment on "Ultraviolet Completion of the Big Bang in Quadratic Gravity"
Abstract
We examine the round Euclidean no-boundary saddle proposed by Liu, Quintin, and Afshordi in "Ultraviolet Completion of the Big Bang in Quadratic Gravity." For a free, massless, conformal realization of their large matter sector, the omitted type-A trace anomaly contributes at leading order in the matter multiplicity. Within the one-loop renormalization-group-improved pure quadratic truncation, both the sphere effective action and the local trace equation show that a stationary point of the running R2 coupling supports a round sphere only if the total Euler anomaly coefficient vanishes. Using the proposed beta function, we further find that no real stationary coupling ratio exists when this coefficient exceeds 79/420, a bound violated parametrically by the assumed matter sector when the remaining gravitational contributions are perturbatively controlled and of order unity. The local obstruction also applies to a round half-sphere and cannot be removed by shifting its radius. Under these assumptions, the proposed round starting geometry and its stated continuation to Lorentzian inflation are excluded, without ruling out inflation from other initial conditions.
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BibTeX
@misc{shinn2026comment,
title = {{Comment on "Ultraviolet Completion of the Big Bang in Quadratic Gravity"}},
author = {Mark A. Shinn},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26827},
eprint = {2609.26827},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26827},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Comment on "Ultraviolet Completion of the Big Bang in Quadratic Gravity"
AU - Mark A. Shinn
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.26827
UR - https://arxiv.org/abs/2609.26827
AB - We examine the round Euclidean no-boundary saddle proposed by Liu, Quintin, and Afshordi in "Ultraviolet Completion of the Big Bang in Quadratic Gravity." For a free, massless, conformal realization of their large matter sector, the omitted type-A trace anomaly contributes at leading order in the matter multiplicity. Within the one-loop renormalization-group-improved pure quadratic truncation, both the sphere effective action and the local trace equation show that a stationary point of the running R^2 coupling supports a round sphere only if the total Euler anomaly coefficient vanishes. Using the proposed beta function, we further find that no real stationary coupling ratio exists when this coefficient exceeds 79/420, a bound violated parametrically by the assumed matter sector when the remaining gravitational contributions are perturbatively controlled and of order unity. The local obstruction also applies to a round half-sphere and cannot be removed by shifting its radius. Under these assumptions, the proposed round starting geometry and its stated continuation to Lorentzian inflation are excluded, without ruling out inflation from other initial conditions.
ER -