  The discovery of gravitational waves from merging binary black holes has
generated considerable interest in examining whether these black holes could
have a primordial origin. If a significant number of black holes have to be
produced in the early universe, the primordial scalar power spectrum should
have an enhanced amplitude on small scales, when compared to the COBE
normalized values on the larger scales that is strongly constrained by the
anisotropies in the cosmic microwave background. In the inflationary scenario
driven by a single, canonical scalar field, such power spectra can be achieved
in models that permit a brief period of ultra slow roll inflation during which
the first slow roll parameter decreases exponentially. In this review, we shall
consider a handful of such inflationary models as well as a reconstructed
scenario and examine the extent of formation of primordial black holes and the
generation of secondary gravitational waves in these cases. We shall also
discuss the strength and shape of the scalar bispectrum and the associated
non-Gaussianity parameter that arise in such situations. We shall conclude with
an outlook wherein we discuss the wider implications of the increased strengths
of the non-Gaussianities on smaller scales.

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