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

Abstract

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 $R=15h^{-1}\mathrm{Mpc}$, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by $27{\%}_{-5\%}^{+9\%}$ for ${\sigma }_8$ and $26{\%}_{-5\%}^{+7\%}$ 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 ($k_{\max }\simeq 0.16h\mathrm{Mp}{\mathrm{c}}^{-1}$) under three halo-selection conditions: all halos, fixed number density, and mass-selected ($M>3\times 10^{13}{h}^{-1}{M}_{\odot }$). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by $45{\%}_{-9\%}^{+20\%}$ for ${\sigma }_8$ and $43{\%}_{-7\%}^{+10\%}$ 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.

22 pages, 11 figures and 3 tables. Matched to the revised version. Including new results for Power spectrum

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