An optimal estimator for the CMB-LSS angular power spectrum and its application to WMAP and NVSS data

TL;DR

This paper introduces an optimal quadratic maximum likelihood estimator for the CMB-LSS angular power spectrum, demonstrating its accuracy on simulations and applying it to WMAP and NVSS data to constrain dark energy parameters.

Contribution

The paper develops and applies a quadratic maximum likelihood method for estimating the CMB-LSS cross-correlation power spectrum, improving robustness and accuracy over previous approaches.

Findings

The estimator accurately recovers simulated spectra.

Application to WMAP and NVSS data yields constraints on dark energy.

Results favor a universe with a cosmological constant around 70%.

Abstract

We use a Quadratic Maximum Likelihood (QML) method to estimate the angular power spectrum of the cross-correlation between cosmic microwave background and large scale structure maps as well as their individual auto-spectra. We describe our implementation of this method and demonstrate its accuracy on simulated maps. 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. With the correction of the declination systematics in NVSS, we can safely use most of the information contained in this survey. We then 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 WMAP 7 year and NVSS maps with 1.8$^\circ$ resolution, the best-fit model has a cosmological constant of approximatively 70% of the total energy density, disfavouring an Einstein-de Sitter Universe at more than 2 $\sigma$ CL (confidence level).