The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

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Abstract
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. The formula 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 the fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lemaître universe with arbitrary cosmological parameters Ω0 and λ0. We illustrate the pattern of the resulting correlation function with several models, and also show that the validity region of the conventional distant observer approximation is θ ≤ 10°.