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Physical Review D 86 (2012) 076005
CMB EB and TB cross-spectrum estimation via pseudospectrum techniques
J. Grain1, M. Tristram2, R. Stompor3

We discuss methods for estimating EB and TB spectra of the Cosmic Microwave Background anisotropy maps covering limited sky area. Such odd-parity correlations are expected to vanish whenever parity is not broken. As this is indeed the case in the standard cosmologies, any evidence to the contrary would have a profound impact on our theories of the early Universe. Such correlations could also become a sensitive diagnostic of some particularly insidious instrumental systematics. In this work we introduce three different unbiased estimators based on the so-called standard and pure pseudo-spectrum techniques and later assess their performance by means of extensive Monte Carlo simulations performed for different experimental configurations. We find that a hybrid approach combining a pure estimate of B-mode multipoles with a standard one for E-mode (or T) multipoles, leads to the smallest error bars for both EB (or TB respectively) spectra as well as for the three other polarization-related angular power spectra i.e. EE, BB and TE$. However, if both E and B multipoles are estimated using the pure technique the loss of precision for the EB spectrum is not larger than ~30%. Moreover, for the experimental configurations considered here, the statistical uncertainties -- due to sampling variance and instrumental noise -- of the pseudo-spectrum estimates is at most a factor ~1.4 for TT, EE and TE spectra and a factor ~2 for BB, TB and EB spectra, higher than the most optimistic Fisher estimate of the variance.
1:  IAS - Institut d'astrophysique spatiale
2:  LAL - Laboratoire de l'Accélérateur Linéaire
3:  APC - UMR 7164 - AstroParticule et Cosmologie
Sciences of the Universe/Astrophysics/Cosmology and Extra-Galactic Astrophysics

Physics/Astrophysics/Cosmology and Extra-Galactic Astrophysics
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