Optimal inference of cosmological parameters in preparation of the Euclid survey / Optimal extraction of cosmological parameters in the preparation of the Euclid survey

Upcoming cosmological surveys such as Euclid, aim at providing measurements of cosmological observables coming from the Large Scale Structure of the universe with an unprecedented precision. This should help in uncovering the mysteries of modern cosmology, like the origin of the accelerated expansion of the universe and the value of the total neutrino mass. However, to take advantage of such precise measurements, we must control and understand the systematics linked to the different steps of the statistical analyses which are exploited to extract cosmological parameters from the observables. In particular, the theoretical modeling and the covariance matrix of our observables are the most important ingredient of the likelihood function, that is central in the statistical estimation of cosmological parameters. This thesis aims at studying the potential biases on cosmological parameter estimation, coming from a poor modeling of either of these ingredients of the likelihood, in the preparation of the Euclid survey. After setting the general context of precision cosmology and introducing the key theoretical and technical concepts exploited in this thesis, I will present the results of the two analyses that I conducted. A first part of this thesis is dedicated to a study of the biases on the estimation of cosmological parameter posteriors, with the matter power spectrum. In particular I focus on effects induced by: the estimation of the covariance matrix with a finite number of mocks, the non-Gaussian covariance arising from non-linear clustering on small scales and the theoretical modeling of the non-linear power spectrum. As one of the major goals of Euclid is to provide a stringent constraint on the total neutrino mass, I dedicate a particular attention to this parameter, by performing the analysis with state-of-the-art N-body simulations that include massive neutrinos. The second analysis presented in this thesis aims to quantify the effect of the non-Gaussian covariance coming from the correlations between modes inside and outside the survey, called the Super-Sample Covariance (SSC). By forecasting the cosmological constraints coming from a Euclid-like analysis, combining photometric galaxy clustering and weak lensing, I show that SSC accounts for a non-negligible part of the total error budget on cosmological parameters. In addition I present a new method to account for the survey footprint in the computation of SSC. (author)