L'EVOLUZIONE DEGLI OGGETTI COMPATTI E DELLE LORO GALASSIE OSPITI NEL TEMPO COSMICO

Gravitational wave detections allow us to construct a demography of compact objects. These are exotic systems such as stellar-mass black holes and neutron stars. The LIGO-Virgo-KAGRA collaboration has gathered about 90 event candidates with high probability of astrophysical origin, all of them possibly associated with binary compact object mergers. In this Thesis, I explore the evolution of binary compact objects across cosmic time. This topic has become increasingly important in recent years, as the next generation of ground-based detectors is expected to detect binary black hole mergers up to z ∼ 100. In this work, I evaluate the astrophysical rates and the properties of the host galaxies of binary black holes (BBHs), black hole-neutron star binaries (BHNSs) and binary neutron stars (BNSs). Determining their merger rate density evolution is challenging because of various sources of uncertainty. To address this issue, I have developed a code called cosmoRate, which combines catalogues of merging compact objects with an observation-based estimate of the metallicity-specific star formation rate density. This code is highly adaptable and allows for the exploration of different regions of the parameter space that significantly impact the merger rate density. For example, I took into account different formation channels of binary compact objects, such as dynamics or isolated binary evolution. I have found that the merger rate density of dynamically formed BBHs in young star clusters is higher than that of isolated BBHs. This is not the case for BNSs formed in young star clusters, which are less likely to merge because dynamics inhibits their formation. Focusing on the isolated formation scenario, I examined the major sources of uncertainty that affect the merger rate density. For example, the BNS merger rate ranges from ∼ 10^3 to ∼ 20 Gpc^−3 yr^−1 at redshift z ∼ 0, when the common envelope efficiency parameter is varied from α = 7 to 0.5 in our population synthesis code MOBSE. In contrast, the local merger rates of BBHs and BHNSs only change by a factor of ∼ 2 − 3. The main source of uncertainty for the BBH merger rate density is the uncertainty in stellar metallicity evolution, which leads to a variation of (at least) one order of magnitude. The host galaxies of gravitational-wave sources contain valuable insights about the formation and evolution of compact object mergers. To study this topic, I developed a code called galaxyRate, which uses observational scaling relations to estimate the astrophysical rates and host galaxy properties. I obtained the properties of the formation galaxy population from the galaxy stellar mass function, the star- forming main sequence of galaxies, and either the mass metallicity relation or the fundamental metallicity relation. I found that the evolution of the BBH merger rate density is significantly impacted by the choice of both the galaxy main sequence and the metallicity evolution. For example, the BBH merger rate density increases more rapidly when using the mass metallicity relation. I also found that, in general, BBHs tend to form in low-mass, metal-poor galaxies and merge in high-mass, metal-rich galaxies. The next-generation ground-based detectors will explore gravitational-wave sources at high redshift. In preparation for this, I evaluated the merger rate density and evolving mass spectrum of BBHs formed from the first generation of stars (Population III stars). I thoroughly examined a variety of initial conditions, including variations in the orbital properties and initial mass function of Pop. III binary systems, as well as four models of the formation history of Pop. III stars. My analysis revealed that the median merger rate density is 4 Gpc^−3 yr^−1 at z = 8−10, and 0.1 Gpc^−3 yr^−1 at z = 0, with an uncertainty of about four orders of magnitude.