Non-Gaussian Expansion of Minkowski Tensors in Redshift Space

TL;DR

This paper extends Minkowski Tensors analysis to redshift space in cosmology, deriving ensemble averages for non-Gaussian matter fields and validating predictions with simulations to aid parameter estimation.

Contribution

It introduces a perturbative framework for Minkowski Tensors in redshift space, incorporating non-Gaussian effects and validating with dark matter simulations.

Findings

Perturbation theory matches simulation data well at large scales.

Finger-of-God effects significantly impact line-of-sight components.

The approach enables cosmological parameter estimation from galaxy surveys.

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 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< 20 Mpc/h) and are particularly pronounced in the components parallel to the line of sight.