The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter

TL;DR

The paper introduces the Helmholtz Hierarchy, a new formalism for modeling the phase space statistics of cold dark matter, capturing effects like stream crossing and bridging simplified and complex gravitational dynamics.

Contribution

It develops a novel hierarchy of equations that interpolates between approximations and full gravitational interactions, incorporating stream crossing effects.

Findings

Hierarchy is self-consistent and causal to all orders

Provides a new interpretation in terms of effective particle trajectories

Bridges Zel'dovich approximation and full gravitational dynamics

Abstract

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories.