A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory

TL;DR

This paper compares Kinetic Field Theory and Eulerian Standard Perturbation Theory for cosmic structure formation, showing Kinetic Field Theory's resummation advantages and potential for improved non-linear modeling.

Contribution

It provides the first detailed comparison highlighting the qualitative differences and the resummation capabilities of Kinetic Field Theory over Standard Perturbation Theory.

Findings

Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in the free-streaming regime.

The exact free-streaming solution of Kinetic Field Theory cannot be obtained at any finite order of Standard Perturbation Theory.

Kinetic Field Theory offers a better starting point for perturbative non-linear structure formation treatments.

Abstract

We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starting point for a first quantitative comparison is given by the non-interacting regime of free-streaming kinematics. Our results suggest that Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in this regime. We further show that the exact free-streaming solution of Kinetic Field Theory can not be recovered in any finite order of Standard Perturbation Theory. Kinetic Field Theory should therefore provide a better starting point for perturbative treatments of non-linear structure formation.