The integrated 3-point correlation function of cosmic shear

Abstract

We present the integrated 3-point shear correlation function $i{\zeta }_{\pm }$ -- a higher-order statistic of the cosmic shear field -- which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic $M_{\mathrm{ap}}$ measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function ${\xi }_{\pm }$. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model $i{\zeta }_{\pm }$ and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of $i{\zeta }_{\pm }$ and perform a joint analysis with ${\xi }_{\pm }$ for two tomographic source redshift bins with realistic shape-noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of ${\xi }_{\pm }$ and $i{\zeta }_{\pm }$ has the potential to considerably improve parameter constraints from ${\xi }_{\pm }$ alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.

Accepted for publication in MNRAS; v2 matches the accepted manuscript; 18 pages + appendix

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