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The integrated shear 3-point correlation function ζ± is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function ξ± by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate ζ± that is accurate on small angular scales, and that allows to take baryonic feedback effects into account. Our model builds on the realization that the small-scale ζ± is dominated by the non-linear matter bispectrum in the squeezed limit, which can be evaluated accurately using the non-linear matter power spectrum and its first-order response functions to density and tidal field perturbations. We demonstrate the accuracy of our model by showing that it reproduces the small-scale ζ± measured in simulated cosmic shear maps. The impact of baryonic feedback enters effectively only through the corresponding impact on the non-linear matter power spectrum, thereby permitting to account for these astrophysical effects on ζ± similarly to how they are currently accounted for on ξ±. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to ξ±, a combined |$\xi _{\pm }\ \&\ \zeta _{\pm }$| analysis can lead to improvements of order |$20\!-\!40{{\ \rm per\ cent}}$| on the constraints of cosmological parameters such as σ8 or the dark energy equation of state parameter w 0. We find similar levels of improvement on the constraints of the baryonic feedback parameters, which strengthens the prospects for cosmic shear data to obtain tight constraints not only on cosmology but also on astrophysical feedback models. These encouraging results motivate future works on the integrated shear 3-point correlation function towards applications to real survey data. [ABSTRACT FROM AUTHOR]

We present the integrated three-point shear correlation function i ζ± – 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 i ζ± 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 ζ± 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 i ζ± 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. [ABSTRACT FROM AUTHOR]