Mining cosmology with Euclid

Gravitational wave signals from compact binary coalescences offer a powerful and reliable probe of cosmology and General Relativity. To date, the LIGO-Virgo-KAGRA collaboration has provided important cosmological constraints and tested gravity in the strong field regime. The path ahead is even more promising. In fact, LIGO-Virgo-KAGRA is expected to reach design sensitivity in the next few years, and, most importantly, the next generation of interferometers, like Einstein Telescope and Cosmic Explorer, will be able to detect almost all compact binary coalescences in the observable Universe. This large amount of data is expected to have important consequences for our understanding of cosmology and General Relativity, and in this dissertation, we explore a few ways in which we can leverage this data. Moreover, in cosmology, a timely and interesting area of study to explore is the cross-correlation between galaxies and gravitational waves from compact binary coalescences. In fact, one of the major probes in the study of large-scale structure is Euclid, which is currently taking data and will measure the position and redshift of millions of galaxies. By combining these two datasets, we can constrain cosmological parameters using the cross-correlation, and in this thesis, we start to develop tools for such a project. In this dissertation, as a first step, we present the open source code \texttt{GWJulia} to perform Fisher matrix analysis of compact binary coalescence parameters. We, then, consider a set of case studies to compare different Einstein Telescope designs. We compare a 10km triangular configuration with two 15km L-shaped detectors with different orientations and temperatures. We also discuss the accuracy of combinations of parameters, which is very informative for cosmology or population studies. We, then, explore how gravitational wave observations can be a powerful tool to test the existence and properties of primordial black holes, as these objects leave distinctive imprints on the gravitational waveform. Notably, there are no known astrophysical processes that can form sub-solar mass black holes, making their discovery a compelling signal of new physics. In this thesis, our goal is to assess the ability of next-generation gravitational wave detectors to distinguish primordial black holes from stellar black holes and neutron stars. To do so, we compute the maximum luminosity distances at which confident ($\geq 3\sigma$) detections of sub-solar masses or tidal effects are possible. Our results indicate that next-generation detectors will be capable of probing sub-solar mass primordial black holes out to cosmological distances of $z \sim 3$. We present forecasts for the accuracy with which General Relativity can be tested using third-generation ground-based interferometers, focusing on Einstein Telescope and binary black hole mergers. Within a hyperparameter analysis, we investigate the constraints that Einstein Telescope, in its different configurations, can impose on inspiral post-Newtonian coefficients. Our results indicate that Einstein Telescope could achieve an accuracy of $\mathcal{O}(10^{-7})$ on the dipole radiation term and $\mathcal{O}(10^{-3})$ on higher-order post-Newtonian coefficients, for both the triangular and the two L-shaped designs, with $10^4$ catalog events. We also assess the number of detections required to confidently identify deviations from General Relativity at various post-Newtonian orders and for different detector configurations.