Higher order statistics of weak lensing shear and flexion

Dipak Munshi, Joseph Smidt, Alan Heavens, Peter Coles, Asantha Cooray

Research output: Contribution to journalArticlepeer-review

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 multispectrum which compress some of the available information of higher order multispectra. We show how these can be recovered from noisy observational data even in the presence of an 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.

Original languageEnglish
Pages (from-to)2241-2258
Number of pages18
JournalMonthly Notices of the Royal Astronomical Society
Volume411
Issue number4
DOIs
Publication statusPublished - Mar 2011

Keywords

  • gravitational lensing: weak
  • methods: analytical
  • methods: numerical
  • methods: statistical
  • large-scale structure of Universe
  • LARGE-SCALE STRUCTURE
  • SMALL ANGULAR SCALES
  • COSMIC SHEAR
  • DARK-MATTER
  • POWER SPECTRUM
  • ANALYTICAL PREDICTIONS
  • PERTURBATION-THEORY
  • MODEL PREDICTIONS
  • COLLAPSED OBJECTS
  • NON-GAUSSIANITIES

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