The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions

A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions and thus is applicable to any pair with arbitrary angle θ between lines of sight, and arbitrary redshifts, z1, z2, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lemâıtre universe with arbitrary cosmological parameters Ω0 and λ0. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is θ ≤ 10. Subject headings: cosmology: theory — galaxies: distances and redshifts — quasars: general — large-scale structure of universe — methods: statistical Department of Physics, The University of Tokyo, Hongo 7-3-1, Tokyo 113-0033, Japan; and Research Center for the Early Universe, Faculty of Science, The University of Tokyo, Tokyo 113-0033, Japan.