Strong deviations from scale invariance and the appearance of high peaks in the primordial power spectrum have been extensively studied for generating primordial black holes (PBHs) or gravitational waves (GWs). It is also well-known that the effect of non-linearities can be significant in both phenomena. In this paper, we advocate the existence of a general single-field consistency relation that relates the amplitude of non-Gaussianity in the squeezed limit f _NL to the power spectrum and remains valid when almost all other consistency relations are violated. In particular, it is suitable for studying scenarios where scale invariance is strongly violated. We discuss the general and model-independent consequences of the consistency relation on the behavior of f _NL at different scales. Specifically, we study the size, sign and slope of f _NL at the scales where the power spectrum peaks and argue that generally the peaks of f _NL and the power spectrum occur at different scales. As an implication of our results, we argue that non-linearities can shift or extend the range of scales responsible for the production of PBHs or GWs, relative to the window as determined by the largest peak of the power spectrum, and may also open up new windows for both phenomena.

中文翻译：

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非高斯一致性关系及其对峰值的影响


为了产生原初黑洞（PBH）或引力波（GW），对尺度不变性的强烈偏差和原初功率谱中高峰的出现进行了广泛的研究。众所周知，非线性的影响在这两种现象中都可能很显着。在本文中，我们主张存在一种通用的单场一致性关系，该关系与压缩极限中的非高斯性幅度相关f _NL与功率谱相关，并且在几乎所有其他一致性关系被违反时仍然有效。特别适合研究严重违反尺度不变性的场景。我们讨论一致性关系对行为的一般和与模型无关的后果f不同尺度的_NL 。具体来说，我们研究的大小、符号和斜率f _NL在功率谱峰值的尺度上，并认为通常的峰值f _NL和功率谱出现在不同的尺度上。作为我们结果的暗示，我们认为，相对于由功率谱最大峰值确定的窗口，非线性可以改变或扩展负责产生 PBH 或 GW 的尺度范围，并且也可能打开这两种现象的新窗口。