弱非局域引力中Starobinsky吸引子的辐射修正可移除判据
Removability criterion for radiative corrections to the Starobinsky attractor in weakly nonlocal gravity
AI总结：
该研究提出弱非局域引力中Starobinsky吸引子的辐射修正可移除判据，分析其对(n_s,r)平面预测的影响，指出仅R²项可移除，物质诱导修正会偏移预测。
AI中文摘要：
百分比水平的辐射修正可将α吸引子和Starobinsky类模型的预测结果偏移至ACT DR6所偏好的(n_s,r)平面区域。研究表明，决定性性质并非修正的大小，而是其是否可移除。在慢滚N形式体系中，可观测量是ε(N)的泛函，若ε(N)在某区间上相等，则可重构势函数，仅差振幅缩放和正则场平移。满足(V/V')Δ'=常数的更大一类变形可保留主导预测，并为任何提出的变形提供判据。在R+R²的弱非局域完备化中，改进尺度μ=H(φ)使重整化群时间为树级势对数的一半，因此局域单圈流通过该测试，并将模型演化至E模型族V∝(1-e^(-√(2/3)φ/M_pl))^p，其中p=2+K。由于这些超可重整完备化的发散局域β函数是单圈精确的，更高阶局域跑动不会改变这一图像。诱导的n_s偏移为O(ln N/N²)，其中可移除部分为闭式解，其余部分为数值解。判据未保护的e折叠数以相反符号贡献22%的水平。物质诱导修正在领头阶无法通过相同测试，这正是它们会偏移预测的原因。在ACT DR6之后提出的变形中，f(R)中的R^n项给出(V/V')Δ'=O(N^(n-1))，因此仅n=2是可移除的，且所有增大n_s的变形均不满足该判据。对于标准模型物质，可移除通道仅由希格斯非最小耦合确定，量级为O(10^(-11))，因为测量到的振幅将R²的系数设定为5.1×10^8。
英文摘要：
Radiative corrections at the percent level can shift the predictions of $α$-attractor and Starobinsky-like models into the region of the $(n_s,r)$ plane preferred by ACT DR6. We show that the decisive property is not the size of a correction but whether it is removable. In the slow-roll $N$-formalism the observables are functionals of $\eps(N)$, and equality of $\eps(N)$ on an interval reconstructs the potential up to an amplitude rescaling and a shift of the canonical field. A larger class, selected by $(V/V')Δ'={\rm const}$, preserves the leading predictions and provides a criterion for any proposed deformation. In weakly nonlocal completions of $R+R^{2}$ the improvement scale $μ=H(ϕ)$ makes the renormalization-group time one half of the logarithm of the tree potential, so the local one-loop flow passes the test and evolves the model onto the E-model family $V\propto(1-e^{-\sqrt{2/3}\,ϕ/\mpl})^{p}$ with $p=2+K$. Since the divergent local beta functions of these super-renormalizable completions are one-loop exact, no higher-loop local running modifies this picture. The induced shifts are $\ord(\ln N/N^{2})$ in $n_s$, obtained in closed form for the removable part and numerically for the rest. The number of $e$-folds, which the criterion does not protect, contributes at the \red{$22\%$} level with an opposite sign. Matter-induced corrections fail the same test at leading order, which is why they shift the predictions. Among the deformations proposed since ACT DR6, an $R^{n}$ term in $f(R)$ gives $(V/V')Δ'=\ord(N^{n-1})$, so only $n=2$ is removable, and no deformation that increases $n_s$ satisfies the criterion. For Standard Model matter, the removable channel is fixed by the Higgs nonminimal coupling alone and is $\ord(10^{-11})$, because the measured amplitude sets the coefficient of $R^{2}$ to $5.1\times10^{8}$.
