Toward accurate and precise cosmology with galaxy redshift surveys

Maximizing the extraction of cosmological information while ensuring accurate modeling is essential in the era of precision galaxy surveys. This thesis contributes to both aspects. First, we examine the accuracy of common approximations—such as the plane-parallel and flat-sky assumptions—showing that they can bias cosmological parameter estimates, and we propose alternative models, including a Radial 3D approach and an unequal-time formalism, that preserve three-dimensional clustering information with minimal complexity. Second, we investigate innovative methods and statistics such as field level inference, the galaxy trispectrum, and the marked power spectrum, aimed at extracting additional information on top of the conventional analyses. Although these capture higher-order correlations, we find that the improvement beyond standard analyses is limited. Taken together, these results help to clarify the strengths and limitations of current modeling strategies and suggest directions for the analysis of forthcoming high-precision survey data.