Covariance matrix estimation for the statistics of galaxy clustering

During my Ph.D, my research activity has been mainly focused on the statistical analysis of the large-scale distribution of galaxies. The accurate determination of the cosmological parameters has become one of the key activities in modern cosmology. Choosing between different models requires accurate theoretical predictions of the observables and precise modeling of their statistical uncertainties. In the first part of the thesis I focused my attention on the study of systematic effects, such as galactic extinction, on the clustering of biased tracers of the cosmic density field, e.g. galaxies, that will be of capital importance for future surveys. I have built an analytic model to account for the effects of a generic foreground and we have measured the 2-point function in Fourier space and computed its covariance matrix using a large set (10’000) of synthetic realizations, run with the approximated method PINOCCHIO. I have analyzed all the corrections to the power spectrum and its covariance due to the presence of this foreground, including its coupling with the cosmological signal. This analysis has been published in a JCAP paper this years (Colavincenzo et al. 2017). Then I focused on the Euclid “Covariance comparison projects”, aimed at testing if covariance matrices of clustering measures, obtained with various approximated methods, are unbiased; I want to quantify their impact on the errors on cosmological parameters. I am in charge of the bispectrum covariance matrix comparison (Colavincenzo et al. in prep.). In the second part of this thesis I have used the large set of simulated galaxy catalogs I have access to test models of the galaxy power spectrum covariance matrix. In particular, I aim to get an analytic expression for the non-linear galaxy power spectrum covariance matrix (colavincenzo et al. in prep.). These same catalogs can be used to perform a likelihood analysis on the galaxy bias parameters using the bispectrum covariance matrix. The joint analysis of power spectrum and bispectrum can be used to improve the constraints on cosmological and galaxy bias parameters.