Likelihood Analysis of CMB Temperature and Polarization Power Spectra

Hamimeche, Samira and Lewis, Antony (2008) Likelihood Analysis of CMB Temperature and Polarization Power Spectra. Physical Review D, 77 (10). ISSN 1050-2947

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Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial-sky coverage correlates power spectrum estimators at different l, and the likelihood function for a theory spectrum given a set of observed estimators is non-Gaussian. An accurate analysis must model all these properties. Most existing likelihood approximations are good enough for a temperature-only analysis, however they cannot reliably handle temperature-polarization correlations. We give a new general approximation applicable for correlated Gaussian fields observed on part of the sky. The approximation models the non-Gaussian form exactly in the ideal full-sky limit and is fast to evaluate using a precomputed covariance matrix and set of power spectrum estimators. We show with simulations that it is good enough to obtain correct results at l¿30 where an exact calculation becomes impossible. We also show that some Gaussian approximations give reliable parameter constraints even though they do not capture the shape of the likelihood function at each l accurately. Finally we test the approximations on simulations with realistically anisotropic noise and asymmetric foreground mask.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Depositing User: Antony Lewis
Date Deposited: 06 Feb 2012 21:02
Last Modified: 02 Jul 2019 20:38

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