Non-Gaussian Expansion of Minkowski Tensors in Redshift Space

Abstract

This paper focuses on extending the use of Minkowski Tensors to analyze anisotropic signals in cosmological data, focusing on those introduced by redshift space distortion. We derive the ensemble average of the two translation-invariant, rank-2 Minkowski Tensors ($W_1^{0,2}$ and $W_2^{0,2}$) for a matter density field that is perturbatively non-Gaussian in redshift space. This is achieved through the Edgeworth expansion of the joint probability density function of the field and its derivatives, expressing the ensemble averages in terms of cumulants up to cubic order. Our goal is to connect these theoretical predictions to the underlying cosmological parameters, allowing for parameter estimation by measuring them from galaxy surveys. The work builds on previous analyses of Minkowski Functionals in both real and redshift space and addresses the effects of Finger-of-God velocity dispersion and shot noise. We validate our predictions by matching them to measurements of the Minkowski Tensors from dark matter simulation data, finding that perturbation theory is a qualified success. Non-perturbative Finger-of-God effects remain significant at relatively large scales $R_G \lesssim 20 \, h^{-1} \, {\rm Mpc}$ and are particularly pronounced in the components parallel to the line of sight.