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Issue A&A Volume 408, Number 3, September IV 2003 Page(s) 829 - 834 Section Extragalactic astronomy DOI 10.1051/0004-6361:20031035

A&A 408, 829-834 (2003)
DOI: 10.1051/0004-6361:20031035

The consequences of parity symmetry for higher-order statistics of cosmic shear and other polar fields

P. Schneider

Institut für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
(Received 7 May 2003 / Accepted 30 June 2003 )

Abstract
We consider the parity transformation and the consequences of parity invariance on the n-point correlation function of the cosmic shear caused by gravitational lensing by the large-scale structure, or any other polar (or "spin-2") field. The decomposition of the shear field into  E- and B-modes then yields the result that any correlation function which contains an odd number of B-mode shear components vanishes for parity-invariant random shear fields. In particular, this result implies that the expectation value of the third-order cross aperture statistics, , vanishes for parity-invariant shear fields. Therefore, a significant detection of a non-zero value of in a cosmic shear survey does not indicate the presence of B-modes, but of an underestimate of the statistical uncertainty or cosmic variance, or a remaining systematic effect in the shear measurement. We argue that the parity invariance provides a very specific diagnostic of systematic effects in shear data. Our results apply as well to the linear polarization of the cosmic microwave background.

Key words: dark matter -- methods: statistical -- cosmology: miscellaneous -- cosmic microwave background

© ESO 2003

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