Towards accurate cosmological constraints with Euclid: from selection effects to higher-order statistics

This Thesis presents original contributions to two central challenges in the cosmological analysis of large spectroscopic galaxy surveys, with particular focus on the Euclid mission. In the first part, I develop a complete analysis framework for the anisotropic galaxy three-point correlation function (3PCF) in redshift space. I implement an efficient estimator, the anisotropic Slepian–Eisenstein algorithm, in the publicly available code MeasCORR, and an original tree-level perturbation theory model for the redshift-space 3PCF in the Mod3L package, both based on the Tripolar Spherical Harmonics expansion and the 2D FFTLog algorithm. Applying these tools to 298 N-body halo catalogs from the Minerva simulations, I demonstrate that including anisotropic 3PCF multipoles can be helpful to alleviate the degeneracy between the linear growth rate f, linear bias $b_1$​, and the Alcock–Paczyński distortion parameter $\varepsilon$ in both standalone and joint 2PCF+3PCF analyses, with the remaining limitations attributable to the breakdown of the tree-level model on small scales. In the second part, I develop a data-driven methodology to model the Euclid spectroscopic selection function without relying on Deep Field calibration data. The approach uses Self-Organizing Maps to compress the multidimensional space of observational systematics and imprint the inferred selection onto a random catalog. Validated on realistic Euclid-like mock catalogs, the method reproduces the two-point correlation function with systematic residuals below 10% of the statistical uncertainty, meeting internal Euclid requirements. Applied to the first internal spectroscopic data release, it delivers the first clustering measurements from Euclid spectroscopic data, now adopted as the baseline pipeline for the first public data release.