Cosmology with Large Scale Structures using Massive Spectroscopic Surveys

Spectroscopic surveys aim to map large fractions of the Universe to study the Large Scale Structures (LSS). LSS evolution traces the distribution of matter as a result of the tension between the expansion of the Universe and the gravitational forces, which means that LSS can be used to test cosmological and gravity model, in particular the standard model of cosmology ($\Lambda$CDM) with General Relativity (GR). One usual way to study those LSS is to quantify the clustering of the galaxies with the 2-point correlation function (2PCF). The Baryon Acoustic Oscillations (BAO) signature is characterised as a peak in the 2PCF, whose position is related to the Hubble parameter. Moreover, Redshift Space Distortions (RSD) are imprinted in the 2PCF and are used to measure the growth rate of structure of the Universe. In this thesis I measured the growth rate of structure of the emission line galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) from RSD in configuration space. I was able along with the Sloan Digital Sky Survey (SDSS) collaboration to participate to the final cosmological implication of the past 20 years of SDSS. By a combination of probes, the current cosmological parameters were then constrained with a high precision, outpassing the expected constraints for Stage-III dark energy experiment.Moreover I performed a BAO analysis with voids, tracing the underdensities in the quasars (QSO) sample of eBOSS. While the method was shown to bring great improvement on other tracers, it reveals itself more difficult to deal with quasars due to their low density. I was nevertheless able to detect a BAO signal and to provide forecast for a QSO sample from a DESI-like (Dark Energy Spectroscopic Instrument) experiment.