Inflation is an epoch of accelerated expansion of the early universe that resolves the shortcomings of the hot big bang model of cosmology. It also provides a natural mechanism to generate perturbations which lead to anisotropies in the cosmic microwave background (CMB) that eventually grow to form the large scale structure of the current universe. In this talk, I shall discuss certain non-trivial inflationary mechanisms that predict unique observational signatures over large scales of the CMB and over small scales leading to the enhanced production of primordial black holes and secondary gravitational waves. I shall present the observable quantities that arise from the primordial two-point correlations (the power spectra) in these scenarios, and focus on computation of higher order correlations, namely the associated bispectra. I shall illustrate how the study of bispectra provides richer insight into the dynamics of inflation and resolves possible degeneracies among the models of interest. I shall conclude with a summary of the main results and a brief outlook.

References (in chronological order) :
1. H. V. Ragavendra, D. Chowdhury and L. Sriramkumar, Unique contributions to the scalar bispectrum in ‘just enough inflation’, Proceedings of the Workshop on Frontiers in High Energy Physics (University of Hyderabad, Hyderabad, October 14-17, 2019), Eds. A. Giri and R. Mohanta (Springer, Singapore, 2020), pp. 39-47 [arXiv:1906.03942 [astro-ph.CO]].
2. H. V. Ragavendra, D. Chowdhury and L. Sriramkumar, Suppression of scalar power on large scales and associated bispectra, arXiv:2003.01099 [astro-ph.CO].
3. H. V. Ragavendra, P. Saha, L. Sriramkumar and J. Silk, Primordial black holes and secondary gravitational waves from ultraslow roll and punctuated inflation, Phys. Rev. D 103, 083510 (2021) [arXiv:2008.12202 [astro-ph.CO]].
4. H. V. Ragavendra, L. Sriramkumar and J. Silk, Could PBHs and secondary GWs have originated from squeezed initial states?, JCAP 05, 010 (2021) [arXiv:2011.09938 [astro-ph.CO]].
5. H. V. Ragavendra, Accounting for scalar non-Gaussianity in secondary gravitational waves, Phys. Rev. D 105, 063533 (2022) [arXiv:2108.04193 [astro-ph.CO]].