Two‐Point Correlation Function of High‐Redshift Objects: An Explicit Formulation on a Light‐Cone Hypersurface

Abstract

While all the cosmological observations are carried out on a light cone, the null hypersurface of an observer at z=0, the clustering statistics has been properly defined only on the constant-time hypersurface. We develop a theoretical formulation for a two-point correlation function on the light cone and derive a practical approximate expression relevant to the discussion of clustering of high-redshift objects at large separations. As a specific example, we present predictions of the two-point correlation function for the Durham/AAT, SDSS, and 2dF quasar catalogues. We also briefly discuss the effects of adopted luminosity function, cosmological parameters, and bias models on the correlation function on the light cone.