The integrated three-point correlation function of cosmic shear

We present the integrated three-point shear correlation function iζ_± - a higher order statistic of the cosmic shear field - which can be directly estimated in wide-area weak lensing surveys without measuring the full three-point shear correlation function, making this a practical and complementary tool to two-point statistics for weak lensing cosmology. We define it as the one-point aperture mass statistic M_ap measured at different locations on the shear field correlated with the corresponding local two-point shear correlation function ξ_±. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated three-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 iζ_± 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 iζ_± and perform a joint analysis with ξ_± 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 ξ_± and iζ_± has the potential to considerably improve parameter constraints from ξ_± 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.