Higher order statistics for three-dimensional shear and flexion

Dipak Munshi, Thomas Kitching, Alan Heavens, Peter Coles

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a collection of statistics appropriate for the study of spinorial quantities defined in three dimensions, focusing on applications to cosmological weak gravitational lensing studies in three dimensions. In particular, we concentrate on power spectra associated with three- and four-point statistics, which have the advantage of compressing a large number of typically very noisy modes into a convenient data set. It has been shown previously by Munshi & Heavens that, for non-Gaussianity studies in the microwave background, such compression can be lossless for certain purposes, so we expect the statistics we define here to capture the bulk of the cosmological information available in these higher order statistics. We consider the effects of a sky mask and noise, and use Limber's approximation to show how, for high-frequency angular modes, confrontation of the statistics with theory can be achieved efficiently and accurately. We focus on scalar and spinorial fields including convergence, shear and flexion of three- dimensional weak lensing, but many of the results apply for general spin fields.

Original languageEnglish
Pages (from-to)1629-1653
Number of pages25
JournalMonthly Notices of the Royal Astronomical Society
Volume416
Issue number3
DOIs
Publication statusPublished - Sep 2011

Keywords

  • gravitational lensing: weak
  • methods: analytical
  • methods: numerical
  • methods: statistical
  • large-scale structure of Universe
  • WEAK-LENSING SURVEYS
  • LARGE-SCALE STRUCTURE
  • SMALL ANGULAR SCALES
  • COSMIC SHEAR
  • POWER SPECTRA
  • NON-GAUSSIANITY
  • DARK-MATTER
  • ANALYTICAL PREDICTIONS
  • PERTURBATION-THEORY
  • MODEL PREDICTIONS

Cite this