We investigate a model of R²-gravity with a non-minimally coupled scalar field that gives rise to two-stage inflation with a break, that is, with an intermediate stage where inflation momentarily halts. We find that the power spectrum of the primordial curvature perturbation is significantly enhanced at the break scale, which can account for the primordial black hole (PBH) formation, without affecting the CMB constraint on large scales. The behavior of the curvature perturbation is carefully analyzed and we find a few notable new features in the spectrum. In particular, we find that the k³ growth of the spectrum of toward the end of the first stage of inflation. We argue that this is a universal feature common to all two-stage models where the field dominating the second stage is heavy during the first stage. By appropriately tuning the model parameters, we find that our model can realize the scenario of PBHs as the cold dark matter of the Universe. We also find that we can choose the parameters so that the spectrum of the induced gravitational waves from the enhanced curvature perturbation fits the NANOGrav-15yr data of pulsar timing array observation.

中文翻译：

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两阶段暴胀中的增强曲率扰动和原始黑洞形成


我们研究了一个具有非最小耦合标量场的 R ²重力模型，该模型产生有中断的两阶段暴胀，即暴胀暂时停止的中间阶段。我们发现，原初曲率摄动的功率谱在断裂尺度上显着增强，这可以解释原初黑洞（PBH）的形成，而不影响大尺度上的 CMB 约束。仔细分析了曲率扰动的行为，我们在频谱中发现了一些值得注意的新特征。特别是，我们发现，在通货膨胀第一阶段结束时，k ³的频谱增长。我们认为这是所有两阶段模型共有的普遍特征，其中在第一阶段中主导第二阶段的场很重。通过适当调整模型参数，我们发现我们的模型可以实现PBH作为宇宙冷暗物质的场景。我们还发现，我们可以选择参数，使增强曲率摄动产生的诱发引力波的频谱与脉冲星计时阵列观测的NANOGrav-15yr数据相吻合。