Advancing cosmological statistics: from bispectrum multipole mixing to optimized projected correlation functions

Abstract

This thesis presents advanced statistical tools and optimizations for the analysis of largescale structure, focusing on the bispectrum and the projected correlation function. First, we derive general analytical expressions for how the Alcock-Paczynski distortions affect the power spectrum and bispectrum of cosmological fields. We compute explicit mixing coefficients for bispectrum multipoles in the linear approximation, demonstrating that the leading-order effect is a uniform dilation of the wavevector triplet. While the linear approximation is highly accurate for all power spectrum multipoles and the bispectrum monopole, we identify sub-percent level inaccuracies in the bispectrum quadrupole and a failure in the hexadecapole. These analytical results provide a rigorous alternative to numerical schemes, simplifying bispectrum analysis for galaxy surveys and the measurement of the baryon acoustic oscillation peak position. Second, we investigate the optimization of projected correlation function analysis, specifically examining how results depend on the line-of-sight integration limit, pi-max. Utilizing varied halo occupation distribution parameters and cosmological models, we quantify the dependence of Fisher information on the choice of pi-max. We find that the optimal integration limits for maximizing information content often fall within non-standard ranges, spanning from 10 to 100 h-1 Mpc. Together, these studies enhance the precision of cosmological constraints by providing exact analytical frameworks for higher-order statistics and optimized configurations for projected clustering measurements.