Primordial black holes formation and secondary gravitational waves in
  nonminimal derivative coupling inflation
  We study the possibility of the Primordial Black Holes (PBHs) formation with
the aim of finding a considerable fraction of Dark Matter (DM), using the
gravitationally enhanced friction mechanism which arises from a nonminimal
derivative coupling between the scalar field and the gravity. Assuming the
nonminimal coupling parameter as a special function of the scalar field and
considering the potential of natural inflation, we find three parameter sets
that produce a period of ultra slow-roll inflation. This leads to sufficiently
large enhancement in the curvature power spectra to form PBHs. We show that
under the gravitationally enhanced friction mechanism, PBHs with a mass around
${\cal O}\big(10^{-12}\big)M_\odot$ can constitute around $96\%$ of the total
DM and so this class of PBHs can be taken as a great candidate for DM. We
further study the secondary Gravitational Waves (GWs) in our setting and show
that our model predicts the peak of the present fractional energy density as
$\Omega_{GW0} \sim 10^{-8}$ at different frequencies for all the three
parameter sets. This value lies well inside the sensitivity region of some GWs
detectors at some frequencies, and therefore the observational compatibility of
our model can be appraised by the data from these detectors.
