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 $R=15\,h^{-1}\mathrm{Mpc}$, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by $27\%^{+9\%}_{-5\%}$ for $\sigma_8$ and $26\%^{+7\%}_{-5\%}$ for $\Omega_{\mathrm{m}}$ 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 ($k_{\max}\simeq0.16\,h\,\mathrm{Mpc^{-1}}$) under three halo-selection conditions: all halos, fixed number density, and mass-selected ($M>3\times10^{13}\,h^{-1}M_\odot$). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by $45\%^{+20\%}_{-9\%}$ for $\sigma_8$ and $43\%^{+10\%}_{-7\%}$ for $\Omega_{\mathrm{m}}$. We also extend the simulation-based forecast analysis across a continuous range of cosmological parameters and multiple smoothing scales for morphological measures.