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CMB EB and TB cross-spectrum estimation via pseudospectrum techniques

Abstract : 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.
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Contributor : Sabine Starita <>
Submitted on : Monday, November 5, 2012 - 4:31:31 PM
Last modification on : Thursday, November 26, 2020 - 11:40:02 AM

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J. Grain, M. Tristram, Radek Stompor. CMB EB and TB cross-spectrum estimation via pseudospectrum techniques. Physical Review D, American Physical Society, 2012, 86, pp.076005. ⟨10.1103/PhysRevD.86.076005⟩. ⟨in2p3-00748640⟩

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