The Alcock-Paczynski (AP) effect is a geometrical distortion in three-dimensional observed galaxy statistics. In anticipation of precision cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an efficient method to compute the AP-distorted correlations of galaxy number density and peculiar velocity fields for any larger angular scale not relying on the conventionally used plane-parallel (PP) approximation. Here, instead of the usual Legendre polynomial basis, the correlation functions are decomposed using tripolar spherical harmonic basis; hence, characteristic angular dependence due to the wide-angle AP effect can be rigorously captured. By means of this, we demonstrate the computation of the AP-distorted correlations over the various scales. Comparing our results with the PP-limit ones, we confirm that the errors due to the PP approximation become more remarkable as the visual angle of separation between target galaxies, $\mathrm{\Theta }$, enlarges, and especially for the density auto correlation, the error exceeds 10% when $\mathrm{\Theta }\gtrsim 30°$. This highlights the importance of the analysis beyond the PP approximation.

• Received 18 March 2021
• Accepted 19 May 2021

DOI:https://doi.org/10.1103/PhysRevD.103.123534