Observational imprints of enhanced scalar power on small scales in ultra slow roll inflation and associated non-Gaussianities

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.