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 -a ndB-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, D M 3 E , vanishes for parity-invariant shear fields. Therefore, a significant detection of a non-zero value of D M 3 E 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 eect in the shear measurement. We argue that the parity invariance provides a very specific diagnostic of systematic eects in shear data. Our results apply as well to the linear polarization of the cosmic microwave background.
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