Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

The integrated shear 3-point correlation function zeta (+/-) is a higher-order statistic of the cosmic shear field that describes the modulation of the 2-point correlation function xi( )+/- by long-wavelength features in the field. Here, we introduce a new theoretical model to calculate zeta (+/-) 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 zeta (+/-) 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 zeta (+/-) 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 zeta( )+/- similarly to how they are currently accounted for on xi( )+/-. Using a simple idealized Fisher matrix forecast for a DES-like survey we find that, compared to xi (+/-), a combined xi (+/-) & zeta( +/-) analysis can lead to improvements of order 20-40 per cent on the constraints of cosmological parameters such as sigma(8) or the dark energy equation of state parameter omega(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.