Kinetic Field Theory: Exact free evolution of Gaussian phase-space correlations

Abstract

In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial Gaussian correlations between particles have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary $n$-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for further investigations of interacting perturbation theory.

32 pages

References in corpus (10)

• Linear perturbative theory of the discrete cosmological N-body problem
• Using the Zeldovich dynamics to test expansion schemes
• Large-scale structure perturbation theory without losing stream crossing
• Smoluchowski dynamics and the ergodic-nonergodic transition
• Trajectories of point particles in cosmology and the Zel'dovich approximation
• Gravitational Dynamics of an Infinite Shuffled Lattice of Particles
• Perturbation theory via Feynman diagrams in classical mechanics
• Disturbance in weak measurements and the difference between quantum and classical weak values
• Gravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit
• Perturbative interaction approach to cosmological structure formation

Cited by in corpus (14)

• Cosmic Structure Formation with Kinetic Field Theory
• Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics
• Local clustering of relic neutrinos with kinetic field theory
• A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory
• Kinetic Field Theory for Cosmic Structure Formation
• Resummed Kinetic Field Theory: Using Mesoscopic Particle Hydrodynamics to Describe Baryonic Matter in a Cosmological Framework
• Kinetic Field Theory: Perturbation theory beyond first order
• Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum
• Resummed Kinetic Field Theory: a model of coupled baryonic and dark matter
• Kinetic Field Theory: Higher-Order Perturbation Theory
• Renormalization group computation of likelihood functions for cosmological data sets
• Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory
• Kinetic field theory: effects of modified gravity theories with screening mechanisms on non-linear cosmic density fluctuations
• Baryon-photon interactions in Resummed Kinetic Field Theory