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The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure -- the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly non-linear regime. The goal of this series of papers is to make the leap and lay out the steps to perform an actual data analysis with this theoretical tool. Building upon the LDT framework, in this work (Paper I) we demonstrate how to accurately model the Probability Distribution Function (PDF) of a reconstructed Kaiser-Squires convergence field under a realistic mask, that of the third data release of the Dark Energy Survey (DES). We also present how weak lensing systematics and higher-order lensing corrections due to intrinsic alignments, shear biases, photo-$z$ errors and baryonic feedback can be incorporated in the modelling of the reconstructed convergence PDF. In an upcoming work (Paper II) we will then demonstrate the robustness of our modelling through simulated likelihood analyses, the final step required before applying our method to actual data., Comment: 37 pages, 9 figures and 2 tables. Submitted to JCAP, comments welcome

The integrated shear 3-point correlation function $\zeta_{\pm}$ measures the correlation between the local shear 2-point function $\xi_{\pm}$ and the 1-point shear aperture mass in patches of the sky. Unlike other higher-order statistics, $\zeta_{\pm}$ can be efficiently measured from cosmic shear data, and it admits accurate theory predictions on a wide range of scales as a function of cosmological and baryonic feedback parameters. Here, we develop and test a likelihood analysis pipeline for cosmological constraints using $\zeta_{\pm}$. We incorporate treatment of systematic effects from photometric redshift uncertainties, shear calibration bias and galaxy intrinsic alignments. We also develop an accurate neural-network emulator for fast theory predictions in MCMC parameter inference analyses. We test our pipeline using realistic cosmic shear maps based on $N$-body simulations with a DES Y3-like footprint, mask and source tomographic bins, finding unbiased parameter constraints. Relative to $\xi_{\pm}$-only, adding $\zeta_{\pm}$ can lead to $\approx 10-25\%$ improvements on the constraints of parameters like $A_s$ (or $\sigma_8$) and $w_0$. We find no evidence in $\xi_{\pm} + \zeta_{\pm}$ constraints of a significant mitigation of the impact of systematics. We also investigate the impact of the size of the apertures where $\zeta_{\pm}$ is measured, and of the strategy to estimate the covariance matrix ($N$-body vs. lognormal). Our analysis solidifies the strong potential of the $\zeta_{\pm}$ statistic and puts forward a pipeline that can be readily used to improve cosmological constraints using real cosmic shear data., Comment: 21 pages, 11 figures, 3 tables. Comments welcome

We present the integrated 3-point shear correlation function $i\zeta_{\pm}$ -- a higher-order statistic of the cosmic shear field -- which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic $M_{\mathrm{ap}}$ measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function $\xi_{\pm}$. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-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 $i\zeta_{\pm}$ 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 $i\zeta_{\pm}$ and perform a joint analysis with $\xi_{\pm}$ 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 $\xi_{\pm}$ and $i\zeta_{\pm}$ has the potential to considerably improve parameter constraints from $\xi_{\pm}$ 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., Comment: Accepted for publication in MNRAS; v2 matches the accepted manuscript; 18 pages + appendix