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Primordial black holes and secondary gravitational waves from natural inflation

The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at $10^{12}$ Mpc$^{-1}$, $10^{8}$ Mpc$^{-1}$ and $10^{5}$ Mpc$^{-1}$ by adjusting the model parameters. With the enhanced primordial curvature perturbations, we show the production of PBH DM with peak masses around $10^{-13}\ M_{\odot}$, the Earth's mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, $10^{-6}$ Hz and nHz, respectively. The PBHs with the mass scale $10^{-13}\ M_{\odot}$ can make up almost all the DM and the associated SIGWs is testable by spaced based gravitational wave observatory.