# Large-Scale Velocity Dispersion and the Cosmic Web

## TL;DR

This paper investigates the large-scale velocity dispersion tensor in the cosmic web, revealing its environmental dependence, alignment with the tidal field, and potential for classifying cosmic web structures without free parameters.

## Contribution

It introduces a parameter-free dynamical classification of cosmic web components based on the velocity dispersion tensor, aligning well with existing methods.

## Key findings

- Velocity dispersion tensor correlates with cosmic web structures.
- Tensor aligns with the large-scale tidal field.
- Large-scale velocity dispersion is dominated by the largest perturbations.

## Abstract

Gravitational collapse in cosmological context produces an intricate cosmic web of voids, walls, filaments and nodes. The anisotropic nature of collisionless collapse leads to the emergence of an anisotropic velocity dispersion, or stress, that absorbs most of the kinetic energy after shell-crossing. In this paper, we measure this large-scale velocity dispersion tensor $\sigma^2_{ij}$ in $N$-body simulations using the phase-space interpolation technique. We study the environmental dependence of the amplitude and anisotropy of the velocity dispersion tensor field, and measure its spatial correlation and alignment. The anisotropy of $\sigma^2_{ij}$ naturally encodes the collapse history and thus leads to a parameter-free identification of the four dynamically distinct cosmic web components. We find this purely dynamical classification to be in good agreement with some of the existing classification methods. In particular, we demonstrate that $\sigma^2_{ij}$ is well aligned with the large-scale tidal field. We further investigate the influence of small scale density fluctuations on the large scale velocity dispersion, and find that the measured amplitude and alignments are dominated by the largest perturbations and thus remain largely unaffected. We anticipate that these results will give important new insight into the anisotropic nature of gravitational collapse on large scales, and the emergence of anisotropic stress in the cosmic web.