# An optimal estimator for the correlation of CMB anisotropies with Large Scale Structures and its application to WMAP-7year and NVSS

Schiavon, Francesca (2012) An optimal estimator for the correlation of CMB anisotropies with Large Scale Structures and its application to WMAP-7year and NVSS, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Astronomia, 24 Ciclo. DOI 10.6092/unibo/amsdottorato/4793.
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## Abstract

In the thesis we present the implementation of the quadratic maximum likelihood (QML) method, ideal to estimate the angular power spectrum of the cross-correlation between cosmic microwave background (CMB) and large scale structure (LSS) maps as well as their individual auto-spectra. Such a tool is an optimal method (unbiased and with minimum variance) in pixel space and goes beyond all the previous harmonic analysis present in the literature. We describe the implementation of the QML method in the {\it BolISW} code and demonstrate its accuracy on simulated maps throughout a Monte Carlo. We apply this optimal estimator to WMAP 7-year and NRAO VLA Sky Survey (NVSS) data and explore the robustness of the angular power spectrum estimates obtained by the QML method. Taking into account the shot noise and one of the systematics (declination correction) in NVSS, we can safely use most of the information contained in this survey. On the contrary we neglect the noise in temperature since WMAP is already cosmic variance dominated on the large scales. Because of a discrepancy in the galaxy auto spectrum between the estimates and the theoretical model, we use two different galaxy distributions: the first one with a constant bias $b$ and the second one with a redshift dependent bias $b(z)$. Finally, we make use of the angular power spectrum estimates obtained by the QML method to derive constraints on the dark energy critical density in a flat $\Lambda$CDM model by different likelihood prescriptions. When using just the cross-correlation between WMAP7 and NVSS maps with 1.8° resolution, we show that $\Omega_\Lambda$ is about the 70\% of the total energy density, disfavouring an Einstein-de Sitter Universe at more than 2 $\sigma$ CL (confidence level).

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Schiavon, Francesca
Supervisore
Dottorato di ricerca
Scuola di dottorato
Scienze matematiche, fisiche ed astronomiche
Ciclo
24
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
cosmic microwave background - large scale structure - methods: numerical - methods: statistical - cosmology: observations
URN:NBN
DOI
10.6092/unibo/amsdottorato/4793
Data di discussione
20 Aprile 2012
URI