KiDS-1000 cosmology: Combined second- and third-order shear statistics

In this work, we perform the first cosmological parameter analysis of the fourth release of Kilo Degree Survey (KiDS-1000) data with second- and third-order shear statistics. This paper builds on a series of studies aimed at describing the roadmap to third-order shear statistics. We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics MapMapMap in a tomographic set-up. We validated our pipeline with $N$-body mock simulations of the KiDS-1000 data release. To model the second- and third-order statistics, we used the latest version of HMcode2020 for the power spectrum and BiHalofit for the bispectrum. Furthermore, we used an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the MapMapMap part of the data vector. This makes it possible to carry out a data analysis of the KiDS-1000 data release using a combined analysis of COSEBIs and third-order shear statistics. We first validated the accuracy of our modelling by analysing a noise-free mock data vector, assuming the KiDS-1000 error budget, finding a shift in the maximum of the posterior distribution of the matter density parameter, $ Omm $, and of the structure growth parameter, $ S_8 < 0.05\ S_8 $. Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained $ $ and $S_8= Omm/0.3 The geometric average on the errors of Omm and $S_8$ of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.