Probing the nature of Dark Energy through the study of large scale structures using spectroscopic surveys and their simulations

Measurements of large-scale structure (LSS), as performed on the largest 3D map of over two million extragalactic sources from the Sloan Digital Sky Survey, together with measurements of the cosmic microwave background (CMB) anisotropies, are in complete agreement with a flat $\Lambda$CDM Universe. In this model, the accelerating expansion of the Universe is driven by dark energy ($\Lambda$), and galaxies are formed under the gravitational pull of cold dark matter. The precise nature of these two dark components remains unknown. The Dark Energy Spectroscopic Instrument (DESI) aims to unravel the mystery of the former by probing the Universe at different epochs through measurements of LSS. This thesis presents an overview of the necessary steps for studying LSS with spectroscopic surveys, along with my contributions toward building realistic galaxy simulations to estimate covariance matrices, as well as improving and developing models to constrain cosmological parameters from real data.Using the Baryon Acoustic Oscillations (BAO) as a standard ruler, DESI aims to measure the distances of 40 million galaxies and quasars with a sub-percent precision. Achieving such level of precision requires a careful analysis of the systematic effects. Therefore, DESI has initiated a mock challenge to test different methods to construct covariance matrices, which are needed for estimating the precision of the measurements. Chapter 2 presents some techniques to build realistic galaxy simulations starting from simulated dark matter haloes, and how these simulations can be used to compute a covariance matrix.The last section shows that using a Halo Occupation Distribution (HOD) model to assign galaxies to the FastPM dark matter haloes, the resulting galaxy two-point clustering is consistent with the one of the reference N-body simulation. Moreover, the estimated sample covariance matrices are robust against the details of the HOD fitting at the scales of interest for LSS studies.Chapter 3 is dedicated to the study of cosmic voids as tracers of underdense regions. Voids and galaxies have been part of multi-tracer BAO studies that have provided stronger constraints on cosmological parameters than galaxy studies alone. Nevertheless, voids require careful modelling due to the exclusion effect that affects their clustering. Therefore, the last section introduces two new numerical models of the void clustering that yield unbiased BAO measurements when subjected to a series of robustness tests. Moreover, they are preferred over the previous models, according to the Bayesian analysis.