A new method for the Alcock-Paczynski test

Abstract: We argue that from observations alone, only the transverse power spectrum $C_\ell(z_1,z_2)$ and the corresponding correlation function $\xi(\theta,z_1,z_2)$ can be measured and that these contain the full three dimensional information. We determine the two point galaxy correlation function at linear order in perturbation theory. Redshift space distortions are taken into account for arbitrary angular and redshift separations. We discuss the shape of the longitudinal and the transversal correlation functions which are very different from each other and from their real space counterpart. We then go on and suggest how to measure both, the Hubble parameter, $H(z)$, and the angular diameter distance, $D_A(z)$, separately from these correlation functions and perform an Alcock-Paczynski test.