Probing non-Gaussianity in the stochastic gravitational wave background with PTAs and ground-based interferometers

The discovery of gravitational waves (GWs) marked an essential moment in our understanding of the Universe, opening a new era in astronomy. From the first direct detection to the observation of hundreds of such events, each observation has provided invaluable insights into the strong gravity regime. Yet, the quest to fully explore the GW spectrum is far from over. The next major breakthrough on the horizon is the detection of a stochastic gravitational wave background (SGWB), originating from hums of spacetime arising from a superposition of countless unresolved sources. While standard searches assume SGWBs to be Gaussian, several early-Universe scenarios predict intrinsically non-Gaussian backgrounds. In this thesis, we investigate how non-Gaussian signatures of a primordial SGWB manifest in the correlators of present and future gravitational-wave detectors, focusing on Pulsar Timing Arrays (PTAs) and ground-based interferometers. In particular, we first review the theoretical framework for gravitational waves and stochastic backgrounds and then we study in detail the response of both detector families to a SGWB. For PTAs, we analyse the Hellings-Downs curve and compute its variance. For ground-based interferometers, we derive the two-point correlation function between detector pairs. Building on this foundation, we present the original results of this work. We compute for the first time the non-Gaussian contribution to the variance of the Hellings-Downs curve, showing that it carries a measurable imprint of primordial non-Gaussianity. We further derive the four-point correlation function for four distinct ground-based interferometers interacting with a non-Gaussian SGWB, a quantity that has not previously appeared in the literature. Our results demonstrate that non-Gaussian signatures of primordial SGWBs leave measurable signatures in detector correlators, opening a new observational window onto early-Universe physics beyond the standard Gaussian paradigm.