A new method for the Alcock-Paczynski test

When observing galaxies we measure their redshift and angular position. To convert this into a three-dimensional galaxy catalog we must make an assumption to relate the observed redshift to a distance. For small redshift, the simple relation D = z/H₀ can be used. Redshift space distortions (RSD) can be taken into account with a convenient expansion in tripolar spherical harmonics. This gives an accurate description of the correlation function at small scales. Apart from RSD, a wrong measurements of H₀ will just rescale the entire catalog but not distort its clustering properties.

However, if we go out to high redshifts, z>1, non-linear terms in z become relevant, and wrong assumptions about the distance redshift relation can bias the entire catalog. We therefore believe that it is important to analyze the truly observed catalog, either using the C(z1 ,z2) spectra, or the angular correlations functions ξ(θ,z1,z2) to describe the observations, and to compare them with their theoretically obtained counterparts. In this way we truly compare observations with their theoretical modeling.