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

Aims. 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. Methods. We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics < M-ap(3)> 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 e ffect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the < M-ap(3)> 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. Results. 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, Delta Omega(m) < 0.02 sigma(Omega m), and of the structure growth parameter, Delta S-8 < 0.05 sigma(S8). Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained Omega(m) = 0.248(-0.055)(+0.062) and S-8 = sigma(8) root Omega(m)/0.3 = 0.772 +/- 0.022. The geometric average on the errors of Omega(m) and S-8 of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.