We present a concrete realization of the sound speed resonance (SSR) mechanism for primordial black hole (PBH) formation within a specific model of Dirac-Born-Infeld (DBI) inflation. We perform a perturbative approach to phenomenologically construct such a viable DBI inflation model that involves the nonoscillating stage and the oscillating stage, with a type of specific forms of the warp factor and the potential. We show that the continuous but nonsmooth conjunction of sound speed between two stages does not yield manifest effects on the phenomenology of SSR, and thus, our model gives rise to the same PBH mass spectrum as the original predictions of SSR. Additionally, we also demonstrate that the violation of adiabaticity of the Mukhanov-Sasaki equation does not affect the comoving curvature perturbation after Hubble crossing in the nonresonant region. Making use of observational data, we derive various cosmological constraints on the parameter space. Our analyses show that the predicted tensor-to-scalar ratio is typically small, while the amplitude of primordial non-Gaussianity can meet with cosmic microwave background bounds, and additionally, the consistency relation for single-field slow-roll inflation is softly violated in our case due to the small sound speed variations.

中文翻译：

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Dirac-Born-Infeld实现原始黑洞的声速共振机制

我们在 Dirac-Born-Infeld (DBI) 膨胀的特定模型中提出了原始黑洞 (PBH) 形成的声速共振 (SSR) 机制的具体实现。我们使用微扰方法从现象学上构建这样一个可行的 DBI 膨胀模型，该模型涉及非振荡阶段和振荡阶段，具有一种特定形式的扭曲因子和潜力。我们表明，两个阶段之间声速的连续但非平滑连接不会对 SSR 的现象产生明显的影响，因此，我们的模型产生与 SSR 的原始预测相同的 PBH 质谱。此外，我们还证明，在哈勃穿越非共振区域后，违反 Mukhanov-Sasaki 方程的绝热性不会影响共动曲率扰动。利用观测数据，我们推导出参数空间的各种宇宙学约束。我们的分析表明，预测的张量与标量比通常很小，而原始非高斯性的幅度可以满足宇宙微波背景界限，此外，单场慢滚膨胀的一致性关系在我们的情况是由于声速变化很小。