The importance of clustering analysis in future Gravitational Wave surveys

The question at the backbone of the work presented in this thesis is: Will future gravitational wave surveys be an effective tool to constrain cosmology? The short answer is: yes, they will. Of course, this will be detailed and justified throughout the text. Indeed, it is already well known that, thanks to their standard siren property, gravitational waves will be able to provide powerful constraints on dark energy and accurate measurements of the Hubble parameter. In our work we will focus instead on a different, less explored aspect, namely the clustering properties of binary mergers from which gravitational waves are produced. These are the only resolved sources we observed until now and they will dominate future observational campaigns as well. Catalogues provided by future detectors will map them in the full sky and to very high distances, up to the edge of the cosmic dark ages, when the first stars began to form. We will show that the tomographic analysis of the angular power spectrum estimated from the distribution of such sources will provide important information on parameters related with both cosmology and the formation channels of the sources themselves. Throughout the thesis, we will derive forecasts mainly for the Einstein Telescope, a third generation ground-based gravitational wave detector that will become operational in the mid 2030s. The reason for this is that clustering studies require a large number of sources which will be achievable with this kind of detectors. The techniques we will adopt present similarities with the methods currently used in the literature for galaxy survey analyses. There will however also be significant differences and new technical challenges to address. We will look deeply into two main topics: how the clustering of the sources can be modelled and how their observed positions in the sky can be affected by large scale structures. To model the clustering of binary mergers, we will rely on state-of-the art hydrodynamical simulations. These take into account astrophysical processes that lead to binary formation and connect them with the distribution and characteristics of their host galaxies. We will first of all model the clustering through a semi-analytical approach. We will then test our results thanks to direct estimates performed on the catalogues extracted from the simulations themselves. In the computation of the angular power spectrum, we will also pay specific attention to the deformation effects induced by gravitational lensing and peculiar velocities of the source host galaxies. In galaxy surveys, where the distance indicator is the redshift, the latter are known as redshift space distortions. However, for gravitational waves signals we will only directly measure the luminosity distance: to obtain redshifts also for gravitational wave events, we will need electromagnetic counterparts or cross-correlations with external datasets. We want however to avoid this in our work and rely on gravitational wave observations alone. For this reason, space distortion effects will have to be recomputed in luminosity distance space. In this thesis, we will describe in detail the main reasons behind this choice and discuss its implications.