Cosmicflows-4: Environmental Modulation of Peculiar Velocity Dispersion

The work investigates whether the dispersion of galaxy peculiar velocities in the Cosmicflows-4 (CF4) catalogue depends systematically on the local large-scale structure environment. Using neighbour counts within smoothing radii of 5–10 Mpc as a minimal and reproducible density estimator, we compare peculiar-velocity dispersion statistics between low-density and high-density environments. The analysis relies directly on peculiar velocities computed from the difference between CMB-frame recession velocity and Hubble expansion, vpec = Vcmb − H0 D, where distances are taken from the CF4 catalogue. The results show a clear environmental modulation: low-density environments exhibit systematically larger peculiar-velocity dispersions than high-density environments, with a dispersion contrast close to a factor of two: σ(Q1) / σ(Q4) ≈ 1.93 ± 0.10 where Q1 and Q4 correspond to the lowest and highest quartiles of neighbour density. To test the robustness of the signal, several controls are applied, including: volumetric distance cuts measurement-quality subsamples within-distance-bin comparisons permutation null tests redshift-space environment estimators RSD-safe projected environment estimators object-level regression analysis controlling for distance The environmental modulation persists under these tests, suggesting that the effect is not driven by simple distance-dependent noise or catalogue selection effects. Because the statistic used here requires only galaxy positions and peculiar velocities, it provides a simple observational benchmark that can be applied to: cosmological simulations mock catalogues future peculiar-velocity surveys to test models of large-scale structure dynamics and gravitational response. The repository contains: the processed CF4 dataset used in the analysis scripts to reproduce all figures and tables robustness tests and null-test pipelines instructions to regenerate the results on a standard laptop The goal of this work is not to perform a full cosmological inference analysis, but to identify a reproducible observational pattern that can be independently tested with simulations and alternative datasets.