It is discussed in this work to produce primordial black hole (PBH) dark matter (DM) and scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in S-dual inflation. It is shown explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at 10¹², 10⁸ and 10⁵ Mpc^–1, respectively, that the primordial black hole dark matter with peak mass around 10^–13 solar mass, the Earth’s mass and the stellar mass are generated, respectively, and that the scalar induced gravitational wave with peak frequency around mHz, μHz and nHz are created, respectively. The primordial black hole with the mass scale 10^–13 solar mass can make up almost all the dark matter and the associated scalar induced secondary gravitational waves is testable by spaced based gravitational wave observatory.

The amplitude of primordial curvature perturbations on a small scale can become large by the enhancement mechanism with a peak function in the non-canonical kinetic term. We apply the enhancement mechanism to S-dual inflation to produce abundant PBHs and observable scalar induced gravitational waves (SIGWs). The power spectrum on a large scale is consistent with observational constraint, and the power spectrum on a small scale is enhanced to the 0.01. It is possible that either sharp peak or broad peak possesses a different peak shape for the peak function by choosing a different value of q. By adjusting the peak position ϕ_p in the peak function, the power spectrum is enhanced on a different scale, henceforth associated with the generation of SIGWs with a different peak frequency, PBHs with different mass are produced. We choose three different values of ϕ_p to obtain enhance power spectrum at 10¹², 10⁸ and 10⁵ Mpc^–1, respectively. The enhanced curvature perturbation produces PBH DM with peak mass around 10^–13 solar mass, the Earth’s mass and the stellar mass, and SIGW with peak frequency around mHz, µHz and nHz, respectively. The stellar mass PBHs may explain black holes observed by LIGO/Virgo collaboration, and the earth-mass PBHs may explain the planet 9. The PBH with the mass scale 10^–13 solar mass can make up almost all the dark matter. The SIGW with the peak frequency around nHz is testable by pulsar timing array observations, and SIGW with the peak frequency around mHz is testable by space based GW observatory. The results show that the enhancement mechanism with a peak function in the non-canonical kinetic term works for S-dual inflation.