Higher-order moments of the lensing shear and other spin two fields

Abstract

We present a method for defining higher-order moments of a spin-2 field on the sky using the transformation properties of these statistics under rotation and parity. For the three-point function of the cosmic shear we show that the eight logically possible combinations of the shear in three points can be divided into two classes, four combinations are even under parity transformations and four are odd. We compute the expected value of the even parity ones in the non-linear regime using the halo model and conclude that on small scales of the four combinations there is one that is expected to carry most of the signal for triangles close to isosceles. On the other hand, for collapsed triangles all four combinations are expected to have roughly the same level of signal although some of the combinations are negative and others positive. We estimate that a survey of a few square degrees area is enough to detect this signal above the noise at arc minute scales.

7 pages, 6 figures. Replaced with revised version. Mistake on symmetry properties of odd parity three point functions fixed

References in corpus (3)

• Halo Models of Large Scale Structure
• Analysis of two-point statistics of cosmic shear: I. Estimators and covariances
• The three-point correlation function of cosmic shear: I. The natural components

Cited by in corpus (36)

• Observational Probes of Cosmic Acceleration
• Cosmology with cosmic shear observations: a review
• CFHTLenS: Cosmological constraints from a combination of cosmic shear two-point and three-point correlations
• Cosmology Constraints from the Weak Lensing Peak Counts and the Power Spectrum in CFHTLenS
• Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications
• Probing Cosmology with Weak Lensing Minkowski Functionals
• Emulating the CFHTLenS Weak Lensing data: Cosmological Constraints from moments and Minkowski functionals
• Weak lensing cosmology with convolutional neural networks on noisy data
• Detection of dark matter Skewness in the VIRMOS-DESCART survey: Implications for Ω_0
• Cosmological parameters from combined second- and third-order aperture mass statistics of cosmic shear
• Cosmology with Minkowski functionals and moments of the weak lensing convergence field
• Constraining neutrino mass with tomographic weak lensing one-point probability distribution function and power spectrum
• The three-point correlation function of cosmic shear. II: Relation to the bispectrum of the projected mass density and generalized third-order aperture measures
• Optimal capture of non-Gaussianity in weak lensing surveys: power spectrum, bispectrum and halo counts
• CMB Lensing Beyond the Power Spectrum: Cosmological Constraints from the One-Point PDF and Peak Counts
• Weak Lensing Minima and Peaks: Cosmological Constraints and the Impact of Baryons
• Cosmological constraints from the capture of non-Gaussianity in Weak Lensing data
• Weak Lensing of the CMB by Large-Scale Structure
• Reducing the shear
• The consequences of parity symmetry for higher-order statistics of cosmic shear and other polar fields
• Denoising Weak Lensing Mass Maps with Deep Learning
• Noise reduction for weak lensing mass mapping: An application of generative adversarial networks to Subaru Hyper Suprime-Cam first-year data
• Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the Universe
• Self-calibration of weak lensing systematic effects using combined two- and three-point statistics
• Analytical Predictions for Statistics of Cosmic Shear: Tests Against Simulations
• A comparative study of cosmological constraints from weak lensing using Convolutional Neural Networks
• A roadmap to cosmological parameter analysis with third-order shear statistics III: Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data
• Halo asphericity and the shear 3-pt function
• The cosmic shear three-point functions
• How well do third-order aperture mass statistics separate E- and B-modes?
• Dark Energy Survey Year 3 Results: Cosmological constraints from second and third-order shear statistics
• A new third-order cosmic shear statistics: Separating E/B-mode correlations on a finite interval
• Explicit computation of shear three-point correlation functions: the one-halo model case
• Detecting Modeling Bias with Continuous Time Flow Models on Weak Lensing Maps
• Non-Gaussian statistics in galaxy weak lensing: compressed three-point correlations and cosmological forecasts
• Dark Energy Survey Year 3 Results: Three-Point Shear Correlations and Mass Aperture Moments