AI 中文总结
本文指出二次引力中提出的无边界圆球起点因迹反常贡献在参数范围内被排除，但不排除其他初始条件下的暴胀。
AI 中文摘要
我们考察了Liu、Quintin和Afshordi在《二次引力中大爆炸的紫外完备化》中提出的圆形欧几里得无边界鞍点。对于其大物质扇区的一种自由、无质量、共形实现，被省略的A型迹反常以物质多重性的领头阶贡献。在一圈重整化群改进的纯二次截断内，球面有效作用和局部迹方程均表明，运行中的$R^2$耦合的驻点仅在总Euler反常系数为零时才支持圆球。使用所提出的beta函数，我们进一步发现当该系数超过$79/420$时，不存在实的驻点耦合比，而这一界限被假定的物质扇区在剩余引力贡献受到微扰控制且量级为1时参数性地违反。局部障碍同样适用于圆半球，且无法通过平移其半径来消除。在这些假设下，所提出的圆形起始几何及其所述的延续到洛伦兹暴胀被排除，但这并不排除从其他初始条件出发的暴胀。
英文摘要
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.
CommentsComment on arXiv:2510.18733
