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

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 $z\lesssim 0.08$ ($\simeq 350\mathrm{M}\mathrm{p}\mathrm{c}$ $h^{-1}$). 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 ${\zeta }_{\rho }(1)\simeq 0.3$ ($D_{\rho }\approx 3.7$) and ${\zeta }_v(1)\simeq 0.4$. The correlation function follows $\xi (r)\sim r^{-1.4}$ over $[45,250]\mathrm{M}\mathrm{p}\mathrm{c}{h}^{-1}$, implying $D_2\simeq 1.6$. Non-linear $\zeta (q)$ and Lévy-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.