Empirical signatures of velocity and density cascades in the Local Universe probed by the CosmicFlows4 dataset
Aims: Our aim is 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 towards large-scale homogeneity within the range probed by current data. Methods: We analysed the Cosmicflows-4 three-dimensional velocity and density-contrast cubes using absolute structure functions of arbitrary order, $q$. The analysis was performed within a volume extending to $z \lesssim 0.08$ ($\simeq 350~\mathrm{Mpc}$ $h^{-1}$). Structure function scaling exponents $\zeta(q)$ were estimated from configuration-space statistics. Intermittency was characterised using the universal multifractal formalism, and the probability density functions of increments were examined. Results: Two regimes were detected. Small separations are dominated by reconstruction smoothing and show a 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 probability density functions (PDFs) indicate intermittency and strong non-Gaussianity. The velocity increments show a systematic negative skewness suggestive of a cascade-like asymmetry associated with amplification of negative compressive gradients.