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. The formula is applicable to any pair with arbitrary angle theta between lines of sight, and arbitrary redshifts z(1), z(2), 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-Lemaitre universe with arbitrary cosmological parameters Omega(0), and lambda(0). 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 a theta less than or equal to 10 degrees.