Investigating parity violation in cosmology

Parity symmetry is broken in the standard model of particle physics. This already prompts the possibility of searching for parity violating signatures in cosmological observables, in case where dark matter (or dark energy) and, most probably, inflation models are rooted in some high-energy theories. Indeed in the last years such a topic has focused much attention, given different observational hints, some of them at more than 4 sigma, of parity violation in cosmological phenomena from the co called cosmic-birefringence of Cosmic Microwave Background photons to the searches for parity violating signatures in the higher-order spatial correlation functions of galaxies on cosmological scales. Typically in cosmology such features entail the emergence of new physics (e.g. parity violation in the gravitational sector, i.e. in the primordial gravitational waves from inflation, due to a modification of Einstein equations, or in a new scalar sector). This thesis will in particular investigates the possibility of generating parity violating features in terms of a four-point correlation function of inflationary curvature perturbations in an inflationary model featuring a phase of ultra slow-roll, which is related to black hole production.