Probing the geometry and the evolution of the Universe with Cosmic Voids

In recent decades, the large-scale distribution of galaxies has emerged as one of the most informative sources for addressing open questions in cosmology, particularly regarding the Universe’s dark components: dark matter and dark energy. The study of the statistical proper- ties of this distribution, known as Galaxy Clustering, can also encompass the distribution of underdense regions that dominate the Universe by volume: cosmic voids. This doctoral Thesis investigates the void-galaxy cross-correlation function, which de- scribes the density profile of galaxies within these voids, representing void shape. In an isotropic universe, cosmic voids should, on average, appear spherical, reflecting the Uni- verse’s large-scale isotropy. However, observed distortions—specifically Redshift Space Distortions (RSD) and Alcock-Paczyn ́ski (AP) effects—disrupt this symmetry. The first, RSD, is a dynamical distortion driven by the growth rate of structures, while the second, AP, is a geometrical distortion arising from deviations of the assumed fiducial cosmological model from the true one. This Thesis applies models of these distortions to infer cosmological parameters and includes a forecast analysis to estimate the constraints achievable with forthcoming data from the Nancy Grace Roman Space Telescope. Furthermore, a novel method is introduced to disentangle these two distortional effects, enhancing parameter constraints by employing reconstruction techniques based on the Zel’dovich approximation. This approach effectively mitigates RSD, which are degenerate with AP distortions, thereby significantly improving statistical significance and accuracy by increasing the number of voids matched by the modelling.