Simulation-Based Inference Quantifies Large-Scale Structure Morphology

This paper presents a simulation-based forecasting analysis comparing the cosmological constraining power of higher-order summary statistics of the large-scale structure: Minkowski Functionals (MFs) and Conditional Moments of Derivatives (CMD). The analysis focuses on their sensitivity to nonlinear and anisotropic features in redshift space, comparing them to the redshift-space halo power spectrum multipoles (PS). The study utilizes halo catalogs from the Big Sobol Sequence simulations at redshift z=0.5, employing a likelihood-free inference framework implemented via neural posterior estimation. The results indicate that CMD provides systematically tighter constraints than MFs at a Gaussian smoothing scale of R=15 h^-1 Mpc. Combining MFs and CMD into a joint estimator improves the precision for sigma_8 and Omega_m relative to MFs alone. In mass-selected configurations, the morphological estimator outperforms the power spectrum. The analysis extends across a continuous range of cosmological parameters and multiple smoothing scales for morphological measures. This research highlights the complementary information captured by different morphological measures and their potential for improving cosmological constraints. Further investigation into the optimal combination of these measures and their application to observational data could lead to significant advancements in our understanding of the universe's composition and evolution.

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