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

Abstract

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 $Ω_m$, $n_s$, and $σ_8$, finding that they probe strongly degenerate combinations of $Ω_m$ and $n_s$, while also exhibiting sensitivity to $σ_8$ through the non-Gaussianity of the evolved density field.

Figures (11)

• Figure 1: Morphological statistics measured from Gaussian random field realisations smoothed on a scale of $R_G = 10\,h^{-1}\,\mathrm{Mpc}$ with a Gaussian filter. Top row: The four Minkowski Functionals, shown by black curves with error bars indicating the $1\sigma$ scatter among realisations. Middle row: The two Minkowski Tensors $W^{0,2}_1$ (left) and $W^{0,2}_2$(middle), and the three Betti numbers (right). Bottom row (left to right): Local statistics: the effective size $(R^{{\rm con},{\rm cav}}_{\rm eff})$, and the shape parameters $(\beta_J^{{\rm con},{\rm cav}\,(1)})$ and $(\beta_J^{{\rm con},{\rm cav}\,(2)})$. Connected components and cavities are shown in red and blue, respectively, while darker and lighter curves correspond to the two $\beta$ eigenvalue ratios extracted from each Minkowski Tensor.
• Figure 2: Morphological statistics measured for gravitationally evolved dark matter fields as a function of iso-field threshold $\nu$. Coloured curves show the dark matter results, while the grey curves correspond to the Gaussian case from Figure \ref{['fig:1_global']} and are included for comparison. The panel layout and colour scheme follow Figure \ref{['fig:1_global']}.
• Figure 3: Identical to Figure \ref{['fig:2_global']}, except that the coloured dark matter curves are presented as functions of volume threshold $\nu_{v}$ as opposed to conventional iso-field values $\nu$. The grey Gaussian reference curves are unaffected by the $\nu \to \nu_{v}$ transformation.
• Figure 4: Morphological statistics measured for Gaussian fields in linear redshift space. Coloured curves show the redshift-space results, while the grey curves correspond to the isotropic Gaussian case from Figure \ref{['fig:1_global']} and are included for comparison. The panel layout and colour scheme follow Figure \ref{['fig:1_global']}, except that the second and third rows include additional sub-panels showing the difference between the redshift- and real-space statistics.
• Figure 5: Morphological statistics measured for dark matter fields in non-linear redshift space. Coloured curves show the redshift-space results, while the grey curves correspond to real space dark matter from Figure \ref{['fig:2_global_nuv']} and are included for comparison. The panel layout and colour scheme follow Figure \ref{['fig:2_global_grf']}, including the sub-panels showing the difference between redshift and real space statistics.