Beyond 3x2-point cosmology: the integrated shear and galaxy 3-point correlation functions

We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions (2PCF) by large-scale features in the fields, and which are easy to measure from galaxy imaging surveys. Based on previous works on the shear-only integrated 3PCF, we develop the theoretical framework for modelling 5 new statistics involving the galaxy field and its cross-correlations with cosmic shear. Using realistic galaxy and cosmic shear mocks from simulations, we determine the regime of validity of our models based on leading-order standard perturbation theory with an MCMC analysis that recovers unbiased constraints of the amplitude of fluctuations parameter As and the linear and quadratic galaxy bias parameters b1 and b2. Using Fisher matrix forecasts for a DES-Y3-like survey, relative to baseline analyses with conventional 3x2PCFs, we find that the addition of the shear-only integrated 3PCF can improve cosmological parameter constraints by 20-40%. The subsequent addition of the new statistics introduced in this paper can lead to further improvements of 10-20%, even when utilizing only conservatively large scales where the tree-level models are valid. Our results motivate future work on the galaxy and shear integrated 3PCFs, which offer a practical way to extend standard analyses based on 3x2PCFs to systematically probe the non-Gaussian information content of cosmic density fields.