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

Understand

In this paper, we introduce a weak, transient and periodical derivative coupling between the inflaton field and gravity, and find that the square of the sound speed of the curvature perturbations becomes a periodic function, which results in that the equation of the curvature perturbations can be transformed into the form of the Mathieu equation in the sub-horizon limit.

• Thus, the parametric resonance will amplify the curvature perturbations so as to generate a formation of abundant primordial black holes (PBHs).
• We show that the generated PBHs can make up most of dark matter.
• Associated with the generation of PBHs, the large scalar perturbations will give rise to the scalar induced gravitational waves which may be detected by future gravitational wave projects.