AI 中文总结
该研究探讨张量诱导反作用对单场暴胀模型中原初黑洞产生的影响，通过自洽反作用方程分析，证实其可限制ε抑制、减小标量功率谱增强并降低相关微调。
AI 中文摘要
我们探讨了微扰理论二阶近似下的张量诱导反作用对单场暴胀模型中原初黑洞产生的影响，该模型中，共动曲率功率谱因瞬态超慢滚相位而被放大。尽管在标准慢滚演化中，主导阶微扰修正几乎可忽略，但在非吸引子区域，该修正变得重要，其作用方向是限制第一慢滚参数ε的抑制，并减小标量功率谱的增强。随后，我们超越标准微扰分析，将背景参数视为有效量，其演化由闭合的反作用方程组自洽确定。该分析对微扰处理之外的效应进行了部分重求和，通过在反作用评估中考虑背景的有效演化，一致表明该效应仍重要，证实了对ε抑制的限制。最后，我们讨论了考虑张量诱导反作用后，与标量功率谱峰值振幅相关的微调被大幅降低。
英文摘要
We discuss the impact of tensor-induced backreaction at second order in perturbation theory on primordial black holes production in single-field inflationary models, where the comoving curvature power spectrum is amplified by a transient ultra-slow-roll phase. Although the leading perturbative correction is mostly negligible in standard slow-roll evolution, it becomes important in non-attractor regimes, going in the direction of limiting the suppression of the first slow-roll parameter $\varepsilon$ and reducing the enhancement of the scalar power spectrum. We then go beyond the standard perturbative analysis by considering the background parameters as effective quantities with evolution self consistently determined by a closed system of backreaction equations. This analysis, which leads to a partial resummation of the effect beyond the perturbative treatment, confirms the limitation of the suppression of $\varepsilon$ by consistently showing how the effect remains important even after accounting for the effective evolution of the background in the evaluation of the backreaction itself. Finally, we discuss how, taking into account the tensor-induced backreaction, the fine-tuning associated with the value of the peak amplitude of the scalar power spectrum is strongly reduced.
Comments8 pages, 3 figures
