Primordial black holes and scalar induced gravitational waves from sound speed resonance in non-minimal derivative coupling inflation model

We investigate an inflationary model with a non-minimal derivative coupling, where the coupling function contains both constant and periodic components. On large scales, the model is in excellent agreement with the latest Planck-ACT-LiteBIRD-BICEP/Keck 2018 (P-ACT-LB-BK18) observations. On small scales, the periodic component induces a sound-speed resonance mechanism that significantly amplifies curvature perturbations, resulting in the production of primordial black holes (PBHs). By incorporating nonlinear effects in the PBH abundance calculation, we find that the resulting PBHs can account for the majority of dark matter in the Universe. Furthermore, the PBH formation process generates scalar-induced gravitational waves (SIGWs) with a characteristic multi-peak spectral shape, which may be detectable by future space-based detectors such as LISA, Taiji, and TianQin. The model also predicts a high-frequency stochastic gravitational-wave background (SGWB) from PBH binary mergers. A combined detection of SIGWs and high-frequency gravitational waves (GWs) in future experiments would provide a direct and testable probe of this inflationary scenario.