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 Gamma((i)) and the third-order aperture statistics < M-ap(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. 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 Omega(m)-sigma(8) plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics.