A roadmap to cosmological parameter analysis with third-order shear statistics I: Modelling and validation

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 ${\mathrm{\Gamma }}^{(i)}$ and the third-order aperture statistics $⟨{\mathcal{M}}_{\mathrm{a}\mathrm{p}}^3⟩$ from the BiHalofit 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. 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 ${\mathrm{\Omega }}_{\mathrm{m}}$-${\sigma }_8$ plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics. Our modelling pipeline is publicly available at https://github.com/sheydenreich/threepoint/releases/.