A redshift‐distortion‐free correlation function at third order in the non‐linear regime

ABSTRACT

The zeroth‐order component of the cosine expansion of the projected three‐point correlation function is proposed for the clustering analysis of cosmic large‐scale structure. These functions are third‐order statistics but can be measured similarly to the projected two‐point correlations. Numerical experiments with N‐body simulations indicate that the advocated statistics are redshift distortion free within 10 per cent in the non‐linear regime on scales of ∼0.2–10 h⁻¹ Mpc. The halo model prediction of the zeroth‐order component of the projected three‐point correlation function agrees with simulations within ∼10 per cent. This lays the ground for using these functions to perform joint analyses with the projected two‐point correlation functions, exploring galaxy clustering properties in the framework of the halo model and relevant extensions.