Empirical signatures of velocity and density cascades in the Local Universe probed by CosmicFlows4 dataset

TL;DR

This study analyzes the multiscale statistical properties of velocity and density fields in the local universe using CosmicFlows4 data, revealing scaling regimes, intermittency, and cascade-like features in cosmic structures.

Contribution

It provides the first detailed characterization of velocity and density cascades in the local universe through structure function analysis and multifractal formalism.

Findings

Identification of two distinct scaling regimes in the data.

Detection of intermittency and non-Gaussianity in cosmic fields.

Evidence of cascade-like asymmetries in velocity gradients.

Abstract

Aims: We aim to characterise the multiscale statistical properties of the reconstructed velocity and density fields of the nearby universe, identify possible scaling regimes, quantify intermittency, and assess indications for the transition toward large-scale homogeneity within the range probed by current data. Methods: We analyse the CosmicFlows4 three-dimensional velocity and density-contrast cubes using absolute structure functions of arbitrary order, $q$. The analysis is performed within a volume extending to $z \lesssim 0.08$ ($\simeq 350~\mathrm{Mpc}$ $h^{-1}$). Structure function scaling exponents $\zeta(q)$ are estimated from configuration-space statistics. Intermittency is characterised using the Universal Multifractal formalism, and probability density functions of increments are examined. Results: Two regimes are detected. Small separations are dominated by reconstruction smoothing and show nearly linear $\zeta(q)$ behaviour. At larger separations, a scaling regime appears with $\zeta_\rho(1)\simeq0.3$ ($D_\rho\approx3.7$) and $\zeta_v(1)\simeq0.4$. The correlation function follows $\xi(r)\sim r^{-1.4}$ over $[45,250]~\mathrm{Mpc}\,h^{-1}$, implying $D_2\simeq1.6$. Non-linear $\zeta(q)$ and L\'evy-stable increment PDFs indicate intermittency and strong non-Gaussianity. Velocity increments show a systematic negative skewness suggestive of a cascade-like asymmetry associated to amplification of negative, compressive gradients.