The enhancement of the spectrum of primordial comoving curvature perturbation $\mathcal{R}$ can induce the production of primordial black holes (PBH) which could account for part of present day dark matter. As an example of the effects of the modification of gravity on the production of PBHs, we investigate the effects on the spectrum of $\mathcal{R}$ produced by the modification of gravity in the case of G-inflation, deriving the relation between the unitary gauge curvature perturbation ζ and the comoving curvature perturbation $\mathcal{R}$, and identifying a background dependent enhancement function $\mathcal{E}$ which can induce large differences between the two gauge invariant variables. We use this relation to derive an equation for $\mathcal{R}$, showing for the presence of a momentum dependent effective sound speed (MESS), associated to the intrinsic entropy which can arise in modified gravity theories, in agreement with the model independent MESS approach to cosmological perturbations.

When ζ is not constant in time it is different from $\mathcal{R}$, for example on sub-horizon scales, or in models exhibiting an anomalous super-horizon growth of ζ, but since this growth cannot last indefinitely, eventually they will coincide. We derive the general condition for super-horizon growth of ζ, showing that slow-roll violation is not necessary. Since the abundance of PBHs depends on the statistics of the peaks of the comoving density contrast, which is related to the spectrum of $\mathcal{R}$, it is important to take into account these effects on the PBHs abundance in modified gravity theories.

原始共同运动曲率摄动谱的增强 $\mathcal{[R}$会诱发原始黑洞（PBH）的产生，这可能是当今暗物质的一部分。作为改变重力对PBHs产生的影响的一个例子，我们研究了对PBHs光谱的影响。$\mathcal{[R}$在G型充气的情况下，通过改变重力来产生，推导了单位尺度曲率摄动ζ和共同运动曲率摄动之间的关系$\mathcal{[R}$，并确定背景相关的增强功能 $\mathcal{E}$这可能会导致两个标准不变变量之间存在较大差异。我们使用这个关系来推导一个方程$\mathcal{[R}$，表明存在与动量相关的有效声速（MESS），与修正的重力理论中可能出现的固有熵相关联，这与模型独立的MESS宇宙扰动方法一致。

当ζ在时间上不是恒定的时，它不同于$\mathcal{[R}$，例如在亚地平线尺度上，或在显示ζ的超地平线异常增长的模型中，但是由于这种增长不能无限持续，因此最终它们会重合。我们得出了ζ的超水平增长的一般条件，表明没有必要违反慢摇。由于PBH的丰度取决于共同移动密度对比的峰的统计数据，这与图谱的光谱有关。$\mathcal{[R}$，重要的是要在修改的重力理论中考虑这些对PBHs丰度的影响。