Beyond 2-Point Statistics: Constraining Cosmology through a Joint 2- and 3- Point Correlation Functions Analysis of BOSS DR12

The study of the Large-Scale Structure of the Universe has become one of the most prominent cosmological probes. Thanks to the advent of large galaxy surveys, we are now able to map our cosmos with unprecedented accuracy; while providing support to the establishment of the ΛCDM model, this progress is also opening new questions in modern cosmology. The increasing volume of data collected by current and future spectroscopic surveys now calls for methods beyond the standard ones to maximise the scientific return of such missions. Clustering analyses suggest that the combination of lower- and higher-order statistics is one of the most promising routes, especially in configuration space where limitations in measurement and theoretical modelling have so far prevented such analyses. In this Thesis, we derive, for the first time on BOSS data, cosmological constraints from a joint analysis of two-point (2PCF) and three-point correlation functions (3PCF), quantifying the gain that can be achieved by including higher-order statistics. We develop a versatile Bayesian pipeline, capable of combining measurements, estimating covariance matrices, computing models, and deriving constraints via an MCMC approach across different configurations. We thoroughly validate this pipeline by creating dedicated synthetic data, testing the robustness of the code, inspecting the degeneracies between parameters, and determining the optimal regimes to minimise them. We apply the pipeline to the BOSS galaxies, fitting the first three multipoles of the 2PCF and the full 3PCF. We derive constraints on the bias, Alcock-Paczyński, and growth of structure parameters in two redshift bins, finding an improvement of a factor of 2 to 5 in the accuracy of the bias parameters from the joint fit. This work demonstrates how crucial it is to include higher-order clustering statistics in future surveys, and contributes to the paper Guidi et al. (including L. Cavazzini) (2026, in prep.).