The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to drive inflation and lead to the amplification of the curvature perturbations. Such an amplification, at wavelengths shorter than those observed in the cosmic microwave background, is necessary in order to have a significant formation of primordial black holes after inflation ends. The technique is applied to the cases of a minimally coupled inflaton, to the nonminimal coupling case and to 𝑓⁡(𝑅) theories of gravity. For such theories, a model dependent analysis of the features leading to the scalar spectrum enhancement is also presented.

中文翻译：

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超电位法和膨胀扰动的放大


超势法是一种重建技术，已被证明可用于构建精确的宇宙学解。我们在这里采用超势方法，以重建膨胀势驱动膨胀并导致曲率扰动放大所需的特征。这种放大的波长比在宇宙微波背景中观察到的波长短，为了在膨胀结束后显着形成原始黑洞是必要的。该技术应用于最小耦合充气的情况、非最小耦合情况和 f（R） 引力理论。对于此类理论，还提出了导致标量谱增强的特征的模型依赖性分析。