Abstract
Over the last two decades, the standard cosmological model "Λ cold dark matter" (ΛCDM) has been firmly established by a variety of observations. Nevertheless, the nature of the dominant components of the Universe - namely dark matter and dark energy - and the process of creation of its initial conditions - namely inflation - are not yet known. Furthermore, as the precision of the data has increased, intriguing anomalies have appeared within the standard cosmological model. These anomalies arise from a discrepancy between the value of some cosmological parameters predicted from their calibration in the distant Universe, for example with the cosmic microwave background (CMB), and the measurement of these parameters from the local Universe. The two most significant tensions in modern cosmology concern the parameter that determines the expansion rate of the Universe, i.e., the Hubble parameter H0, and the parameter that quantifies the amplitude of local matter fluctuations, i.e., the parameter S8. A number of surveys dedicated to measuring large-scale structures (LSS) of the Universe (BOSS and eBOSS in particular, and the forthcoming DESI and EUCLID) can be used to weigh in on these cosmological tensions. The first axis of this thesis is based on a semi-analytical method, known as "effective field theory of large-scale structures" (EFTofLSS), which provides an accurate description of the galaxy power spectrum, and aims at improving cosmological constraints from LSS surveys, a major challenge in the context of the forthcoming data from DESI and Euclid. In particular, we apply an EFTofLSS analysis to describe the BOSS and eBOSS data, and demonstrate that these surveys can be used to obtain constraints that are competitive with those coming from CMB data. We also establish the self-consistency of this theory within the ΛCDM model, as it appears at first sight that the different EFTofLSS parametrizations proposed in the literature seem to provide different constraints on cosmological parameters. We thus identify these discrepancies as originating from subtleties of the commonly used Bayesian framework. In addition, we develop a systematic method for applying the EFTofLSS to different LSS data and obtain robust results contrasting the Bayesian framework with the frequentist approach, for an in depth cosmological inference. The second aspect of my work aims to establish the possible theoretical implications of cosmological tensions for our understanding of the dark sector of the Universe. In particular, we confront various models that can resolve these tensions with the BOSS and eBOSS data analysed under the EFTofLSS. We conclude that current clustering data are not in tension with ΛCDM, and can be used to set important constraints on model suggested to resolve cosmological tensions.