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In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions Γ (i) and the third-order aperture statistics {{{M³ₐp}}} from the B I H ALOFIT bispectrum model and validate these statistics with a series of N -body simulations. We then investigate how to bin the shear three-point correlation functions to achieve an unbiased estimate for third-order aperture statistics in real data. Finally, we perform a cosmological parameter analysis on KiDS1000-like mock data with second- and third-order statistics. In the absence of systematic effects, we recover all cosmological parameters with very little bias. Furthermore, we find that a joint analysis almost doubles the constraining power on S 8 and increases the figure of merit in the Ω m - σ 8 plane by a factor of 5. 9 with respect to an analysis with only second-order shear statistics.
Heydenreich et al. (Wed,) studied this question.