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In this paper, we introduce a weak, transient and periodical derivativecoupling between the inflaton field and gravity, and find that the square ofthe sound speed of the curvature perturbations becomes a periodic function,which results in that the equation of the curvature perturbations can betransformed into the form of the Mathieu equation in the sub-horizon limit.Thus, the parametric resonance will amplify the curvature perturbations so asto generate a formation of abundant primordial black holes (PBHs). We show thatthe generated PBHs can make up most of dark matter. Associated with thegeneration of PBHs, the large scalar perturbations will give rise to the scalarinduced gravitational waves which may be detected by future gravitational waveprojects.

Resonant amplification of curvature perturbations in inflation model with periodical derivative coupling