On the Perturbative Treatment of Interactions in Kinetic Field Theory - Applications to Cosmic Structure Formation

We present the results of applying a perturbative treatment of the interaction operator in the canonical formulation of kinetic field theory (KFT) to cosmic structure formation. The KFT formalism, developed in a series of publications [1–4], allows for the description of equilibrium and non-equilibrium classical many-body systems. The usefulness of KFT for analytical calculations of cosmic structure formation stems from the fact that it circumvents approximations such as the single-stream approximation, which cause more common hydrodynamical frameworks such as Eulerian and Lagrangian perturbation theory to break down at small scales where non-linear structures are forming. This work focuses on a systematic treatment of perturbation theory, which corresponds to an expansion in perturbative corrections to the free phase-space trajectories of the classical point-particles of the system in canonical KFT. We show how diagrams for this perturbation theory can be constructed and evaluated and investigate the different choices for defining free particle trajectories and the corresponding interactions. Results for the dark matter power spectrum are presented and discussed for two such choices, Newtonian and Zel’dovich trajectories. We find that the choice of free trajectories has a substantial impact on the strength of perturbative corrections and specifically that Newtonian trajectories are not well suited to be applied in the canonical formulation of KFT