Morphological Signatures of Gravitational Evolution, Redshift-Space Distortions, and Massive Neutrinos in Large-Scale Structure

We investigate the morphological properties of large-scale structure in the Universe and the physical processes that modify the excursion-set morphology of the three-dimensional matter density field. Using the Quijote N-body simulation suite, we study how an initially Gaussian random matter density field is altered by non-linear gravitational evolution, redshift-space distortions, and massive neutrino free-streaming. To quantify these effects, we employ a comprehensive set of morphological descriptors, including Minkowski Functionals, Betti numbers, Minkowski Tensors, and local measures of the size and shape of connected components and cavities. We find that gravitational evolution, on quasi-linear scales $R_G \sim 10 h^{-1} \mathrm{Mpc}$, strongly skews the one-point distribution and slightly smooths the field via the merging of critical points, with a more pronounced effect for minima and wall saddle points than for peaks. Redshift-space distortions produce the strongest morphological signal, generating pronounced anisotropies that are robustly captured by Minkowski Tensors and local shape measures, arising from both coherent large-scale flows and non-linear Finger-of-God effects. In contrast, massive neutrinos induce an approximately isotropic suppression of small-scale structure, slightly reducing the amplitudes of the Minkowski Functionals while leaving individual shape measures largely unchanged. We further explore the sensitivity of these statistics to variations in cosmological parameters $\Omega_m$, $n_s$, and $\sigma_8$, finding that they probe strongly degenerate combinations of $\Omega_m$ and $n_s$, while also exhibiting sensitivity to $\sigma_8$ through the non-Gaussianity of the evolved density field.