Finding closure: approximating Vlasov-Poisson using finitely generated cumulants

Understand

Since dark matter almost exclusively interacts gravitationally, the phase-space dynamics is described by the Vlasov-Poisson equation.

• A key characteristic is its infinite cumulant hierarchy, a tower of coupled evolution equations for the cumulants of the phase-space distribution.
• While on large scales the matter distribution is well described as a fluid and the hierarchy can be truncated, smaller scales are in the multi-stream regime in which all higher-order cumulants are sourced through nonlinear gravitational collapse.
• This regime is crucial for the formation of bound structures and the emergence of characteristic properties such as their density profiles.