  The violation of the null energy condition (NEC) is closely related to
potential solutions for the cosmological singularity problem and may therefore
play a crucial role in the very early universe. We explore a novel approach to
generate primordial black holes (PBHs) via the violation of the NEC in a
single-field inflationary scenario. In our scenario, the universe transitions
from a first slow-roll inflation stage with a Hubble parameter H = Hinf1 to a
second slow-roll inflation stage with H = Hinf2 > Hinf1, passing through an
intermediate stage of NEC violation. The resulting primordial scalar power
spectrum is naturally enhanced by the NEC violation at a certain wavelength. As
a result, PBHs with masses and abundances of observational interest can be
produced in our scenario. We also examine the phenomenological signatures of
scalar-induced gravitational waves (SIGWs). Our work highlights the
significance of utilizing a combination of PBHs, SIGWs, and primordial
gravitational waves as a powerful probe for exploring the NEC violation during
inflation.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory