The Diffuse Supernova Neutrino Background (DSNB) is the collection of neutrinos emitted from all past core-collapse supernovae, and it has yet to be detected experimentally. An observation of the DSNB can probe the star formation history of the universe, the fraction of black hole-forming supernovae, and even novel neutrino physics phenomena. At present, the Super-Kamiokande (SK) water Cherenkov detector is the most sensitive experiment to detect the DSNB.

The statistics of primordial scalar perturbations play a crucial role in providing phenomenological constraints for new inflationary models. In particular, the probability of unlikely large scalar perturbations (leading to primordial black hole formation) and the concurrent GW backgrounds are very sensitive to the tail of the PDF of primordial curvature perturbations. We analyse such tails in inflationary models featuring an ultra-slow roll phase, known to enhance both the amplitude and non-Gaussianity of curvature perturbations at small scales.

Primordial non-Gaussianities, though yet unobserved, remain an important observable since they can help differentiate various models of inflation. This necessitates a deep understanding of the various processes that could contribute to these non-Gaussianities, with inflationary magnetogenesis being one of them. Often, the spectrum and the bispectrum of the perturbations produced during inflation are studied under the assumption that the metric perturbations can be neglected and that all the relevant physics resides in the coupling of the inflaton and the gauge fields.