Two-point correlation function of high-redshift objects: An explicit formulation on a light-cone hypersurface

While all the cosmological observations are carried out on a light cone, th e 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 c one and derive a practical approximate expression relevant to the discussio n of clustering of high-redshift objects at large separations. As a specifi c example, we present predictions of the two-point correlation function for the Durham/AAT, SDSS, and 2dF quasar catalogues. We also briefly discuss t he effects of adopted luminosity function, cosmological parameters, and bia s models on the correlation function on the light cone.