The integrated three-point correlation function of cosmic shear

We present the integrated three-point shear correlation function i zeta(+/-) - 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 xi(+/-). 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 i zeta(+/-) 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(+/-) and perform a joint analysis with xi(+/-) 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(+/-) and i zeta(+/-) has the potential to considerably improve parameter constraints from xi(+/-) 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.

Automated summary

This study introduces the integrated three-point shear correlation function i zeta(+/-), a higher order statistic of the cosmic shear field that can be directly estimated in wide-area weak lensing surveys, providing a practical and complementary tool for weak lensing cosmology. By developing a theoretical framework and model, and validating it through N-body simulations, the joint analysis of i zeta(+/-) and xi(+/-) is shown to significantly improve parameter constraints and enhance the figure of merit of dynamical dark energy equation of state parameters.