Primordial black holes and secondary gravitational waves from
  inflationary model with a non-canonical kinetic term
  With the enhancement mechanism provided by a noncanonical kinetic term with a
peak, the amplitude of primordial curvature perturbations can be enhanced by
seven orders of magnitude at small scales while keeping to be consistent with
observations at large scales. The peak function and inflationary potential are
not restricted in this mechanism. We use the Higgs model and T-model as
examples to show how abundant primordial black hole dark matter with different
mass and scalar induced secondary gravitational waves with different peak
frequency are generated. We also show that the enhanced power spectrum for the
primordial curvature perturbations and the energy density of the scalar induced
secondary gravitational waves can have either a sharp peak or a broad peak. The
primordial black holes with the mass around $10^{-14}-10^{-12} M_{\odot}$
produced with the enhancement mechanism can make up almost all dark matter, and
the scalar induced secondary gravitational waves accompanied with the
production of primordial black holes can be tested by the pulsar timing arrays
and spaced based gravitational wave observatory. Therefore, the mechanism can
be tested by primordial black hole dark matter and gravitational wave
observations.
