We review the models unifying inflation and Primordial Black Hole (PBH) formation, which are based on the modified (Starobinsky-type) supergravity. We begin with the basic (Starobinsky) inflationary model of modified gravity and its alpha-attractor-type generalizations for PBH production, and recall how all those single-field models can be embedded into the minimal supergravity. Then, we focus on the effective two-field models arising from the modified (Starobinsky-type) supergravity and compare them to the single-field models under review. Those two-field models describe double inflation whose first stage is driven by Starobinsky’s scalaron and whose second stage is driven by another scalar belonging to the supergravity multiplet. The power spectra are numerically computed, and it is found that the ultra-slow-roll regime gives rise to the enhancement (peak) in the scalar power spectrum leading to an efficient PBH formation. The resulting PBH masses and their density fraction (as part of dark matter) are found to be in agreement with cosmological observations. The PBH-induced gravitational waves, if any, are shown to be detectable by the ground-based and space-based gravitational interferometers under construction.

中文翻译：

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膨胀和原始黑洞超重力模型中的多场与单场

我们回顾了基于修正（Starobinsky型）超重力的统一通货膨胀和原始黑洞（PBH）形成的模型。我们从修改重力的基本（Starobinsky）膨胀模型及其对PBH生产的alpha吸引子类型的概括开始，回想一下如何将所有这些单场模型嵌入最小超重力中。然后，我们重点研究由修正的（Starobinsky型）超重力产生的有效两场模型，并将它们与正在审查的单场模型进行比较。这些两场模型描述了双重膨胀，其第一阶段由Starobinsky的标量驱动，第二阶段由另一属于超重力多重性的标量驱动。功率谱是通过数值计算的，并且发现，超慢滚动状态会导致标量功率谱的增强（峰值），从而导致有效的PBH形成。发现所得的PBH质量及其密度分数（作为暗物质的一部分）与宇宙学观察一致。PBH诱导的重力波（如果有的话）显示在建设中的地基和天基重力干涉仪可检测到。