Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference

We perform a simulation-based forecasting analysis to compare the cosmological constraining power of higher-order summary statistics of the large-scale structure, the Minkowski Functionals (MFs) and a class weighted morphological measure known as the Conditional Moments of Derivatives (CMD), with that of the redshift-space halo power spectrum multipoles (PS), with a particular focus on their sensitivity to nonlinear and anisotropic features in redshift space. Our analysis relies on halo catalogs from the Big Sobol Sequence simulations at redshift z=0.5, employing a likelihood-free inference framework implemented via neural posterior estimation. At the fiducial Quijote cosmology and for a Gaussian smoothing scale of R=15,h-1Mpc, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by 27%+9%-5% for σ8 and 26%+7%-5% for Omegam relative to MFs alone, highlighting the complementary anisotropy-sensitive information captured by the CMD in contrast to the scalar morphological content encapsulated by the MFs. We compare the combined statistic MFs+CMD with the PS at matched effective scales (kmaxsimeq0.16,h,mathrmMpc-1) under three halo-selection conditions: all halos, fixed number density, and mass-selected (M>3×1013,h-1M_odot). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by 45%+20%-9% for σ8 and 43%+10%-7% for Omegam. We also extend the simulation-based forecast analysis across a continuous range of cosmological parameters and multiple smoothing scales for morphological measures.