  Primordial black holes (PBHs) can generically form in inflationary setups
through the collapse of enhanced cosmological perturbations, providing us
access to the early Universe through their associated observational signatures.
In the current work we propose a new mechanism of PBH production within
non-canonical inflation, using a class of steep-deformed inflationary
potentials compatible with natural values for the non-canonical exponents. In
particular, by requiring significant PBH production we extract constraints on
the non-canonical exponents. Additionally, we find that our scenario can lead
to the formation of asteroid-mass PBHs, which can account for the totality of
the dark matter, as well as to production of solar-mass PBHs within the
LIGO/VIRGO detection band. Finally, we find that the enhanced cosmological
perturbations which collapse to form PBHs can produce a stochastic
gravitational-wave (GW) background induced by second-order gravitational
interactions. Very interestingly, we obtain a GW signal detectable by future GW
experiments, in particular by SKA, LISA and BBO.
