Exploring the Universe through the astrophysical gravitational-wave background

This thesis is dedicated to the theoretical modelling of the stochastic gravitational-wave background (SGWB) originating from coalescing stellar compact binaries, and its characterization as a tool for studying the properties of binary populations, their host galaxies, and the broader Universe. I defined a general pipeline to obtain theoretical predictions for both the intensity and the anisotropies of the SGWB based on state-of-the-art binary population synthesis codes, empirical prescriptions for galactic physics and a Boltzmann solver for computing the evolution of cosmological perturbations. A key step in the process is the characterization of the SGWB as a tracer of the large-scale structure (LSS), by defining its redshift distribution, bias and magnification bias. Then, I used this pipeline to simulate full-sky maps of the SGWB, taking into account both clustering properties and the discreteness of sources in space and time, which causes the presence of a shot noise that is typically orders of magnitude larger than the intrinsic anisotropies induced by the LSS. An effective way to reduce the impact of shot noise is to cross-correlate the SGWB with other tracers of the LSS. In this thesis, I focused on the cross-correlation with CMB lensing and studied the detectability of the SGWB anisotropies, evaluating the signal-to-noise ratio for the angular power spectrum of both the auto- and cross-correlation, with networks of present and forthcoming gravitational-wave detectors. Finally, I studied how the high-frequency peak of the SGWB produced by coalescing binaries can be used as an observable to constrain a selection of astrophysical and cosmological parameters.