Minkowski Tensors in Redshift Space—Beyond the Plane-parallel Approximation

Abstract The Minkowski tensors (MTs) can be used to probe anisotropic signals in a field, and are well suited for measuring the redshift-space distortion (RSD) signal large-scale structure catalogs. We consider how linear RSD extracted from field without resorting plane-parallel approximation. A spherically distorted is both inhomogeneous. derive expressions two-point correlation functions that elucidate inhomogeneity, then explain breakdown of homogeneity impacts volume ensemble averages tensor functionals. construct average these quantities curvilinear coordinates show approximately equated, but this depends on our choice definition radial distance between observer field. extract functionals distorted, Gaussian random fields gravitationally evolved dark matter density at z = 0 test if we successfully measure Kaiser signal. For find significant, ∼10% anomalous MT component parallel line sight present even large scales R G ≳ 15 Mpc, addition effect. This due line-of-sight being significantly contaminated by Finger God effect, which modeled an additional damping term cumulants.