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

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 $\theta$ 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 fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^ıtre 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 validity region of the conventional distant observer approximation is $\theta \le 10^{\circ }$.

45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000)

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