Higher-order Statistics of Weak Lensing Shear and Flexion

Abstract

Owing to their more extensive sky coverage and tighter control on systematic errors, future deep weak lensing surveys should provide a better statistical picture of the dark matter clustering beyond the level of the power spectrum. In this context, the study of non-Gaussianity induced by gravity can help tighten constraints on the background cosmology by breaking parameter degeneracies, as well as throwing light on the nature of dark matter, dark energy or alternative gravity theories. Analysis of the shear or flexion properties of such maps is more complicated than the simpler case of the convergence due to the spinorial nature of the fields involved. Here we develop analytical tools for the study of higher-order statistics such as the bispectrum (or trispectrum) directly using such maps at different source redshift. The statistics we introduce can be constructed from cumulants of the shear or flexions, involving the cross-correlation of squared and cubic maps at different redshifts. Typically, the low signal-to-noise ratio prevents recovery of the bispectrum or trispectrum mode by mode. We define power spectra associated with each multi- spectra which compresses some of the available information of higher order multispectra. We show how these can be recovered from a noisy observational data even in the presence of arbitrary mask, which introduces mixing between Electric (E-type) and Magnetic (B-type) polarization, in an unbiased way. We also introduce higher order cross-correlators which can cross-correlate lensing shear with different tracers of large scale structures.

16 pages, 2 figures

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Cited by in corpus (15)

• From Weak Lensing to non-Gaussianity via Minkowski Functionals
• Fitting the nonlinear matter bispectrum by the Halofit approach
• On the validity of the Born approximation for weak cosmic flexions
• Higher Order Statistics for Three-dimensional Shear and Flexion
• The Weak Lensing Bispectrum Induced By Gravity
• Analytical shear and flexion of Einasto dark matter haloes
• Weak Lensing Skew-Spectrum
• Estimating the Integrated Bispectrum from Weak Lensing Maps
• Morphology of Weak Lensing Convergence Maps
• Estimate of halo ellipticity as a function of radius with flexions
• Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D
• Position-Dependent Correlation Function of Weak Lensing Convergence
• Intrinsic and extrinsic gravitational flexions
• On the Local-Global Principle for Integral Apollonian-3 Circle Packings
• Local environmental dependence on weak-lensing shear statistics