Minkowski Functionals in Joint Galaxy Clustering & Weak Lensing Analyses

TL;DR

This study assesses the utility of Minkowski functionals applied to clustering and lensing maps in cosmological parameter estimation, finding limited additional information in linear models but potential improvements with nonlinear effects.

Contribution

It explores the combined use of Minkowski functionals on clustering and lensing maps, highlighting their potential and limitations in cosmological analyses.

Findings

MFs do not add information beyond 3x2pt in linear models.

Adding clustering data improves constraints when combined with MFs.

Future work should include nonlinear effects for better constraints.

Abstract

We investigate the inclusion of clustering maps in a weak lensing Minkowski functional (MF) analysis of DES-like and LSST-like simulations to constrain cosmological parameters. The standard 3x2pt approach to lensing and clustering data uses two-point correlations as its primary statistic; MFs, morphological statistics describing the shape of matter fields, provide additional information for non-Gaussian fields. Previous analyses have studied MFs of lensing convergence maps; in this project we explore their simultaneous application to clustering maps. We employ a simplified linear galaxy bias model, and using a lognormal curved sky measurement and Monte Carlo Markov Chain (MCMC) sampling process for parameter inference, we find that MFs do not yield any information in the $\Omega_{\rm m}$ -- $\sigma_8$ plane not already generated by a 3x2pt analysis. However, we expect that MFs should improve constraining power when nonlinear baryonic and other small-scale effects are taken into account. As with a 3x2pt analysis, we find a significant improvement to constraints when adding clustering data to MF-only and MF$+C_\ell$ shear measurements, and strongly recommend future higher order statistics be measured from both convergence and clustering maps.