A redshift distortion free correlation function at third order in the nonlinear regime

TL;DR

This paper introduces a third-order, redshift distortion free correlation function for analyzing cosmic large scale structure, enabling more accurate clustering studies in the nonlinear regime.

Contribution

It proposes a zeroth-order component of the projected three-point correlation function that is free from redshift distortions, validated through simulations and halo model predictions.

Findings

The statistic is redshift distortion free within 10% on scales 0.2-10 Mpc/h.

Halo model predictions agree with simulations within ~10%.

Enables joint analysis with two-point correlations for galaxy clustering studies.

Abstract

The zeroth-order component of the cosine expansion of the projected three-point correlation function is proposed for 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% in the non-linear regime on scales ~0.2-10Mpc/h. Halo model prediction of the zeroth-order component of the projected three-point correlation function agrees with simulations within ~10%. This lays the ground work 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.