# Cosmic Structure Formation with Kinetic Field Theory

## TL;DR

Kinetic Field Theory (KFT) offers a comprehensive statistical framework for modeling cosmic structure formation, incorporating non-linear dynamics, initial conditions, and modified gravity, with applications to both cosmology and atomic physics.

## Contribution

This paper extends KFT to cosmological contexts, develops new analytical methods for non-linear structures, and applies the theory to fluids, dark matter, modified gravity, and atomic systems.

## Key findings

- Derived an analytic, parameter-free equation for the non-linear cosmic power spectrum.
- Developed a resummation scheme for fluid and dark matter mixtures.
- Applied KFT to cold Rydberg atoms, analyzing their spatial correlation functions.

## Abstract

Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of point-like classical particles in or out of equilibrium. We review its application to cosmological structure formation. Beginning with the construction of the generating functional of the theory, we describe in detail how the theory needs to be adapted to reflect the expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, we develop three main approaches to non-linear, late-time cosmic structures, which rest either on the Taylor expansion of an interaction operator, suitable averaging procedures for the interaction term, or a resummation of perturbation terms. We show how an analytic, parameter-free equation for the non-linear cosmic power spectrum can be derived. We explain how the theory can be used to derive the density profile of gravitationally bound structures and use it to derive power spectra of cosmic velocity densities. We further clarify how KFT relates to the BBGKY hierarchy. We then proceed to apply kinetic field theory to fluids, introduce a reformulation of KFT in terms of macroscopic quantities which leads to a resummation scheme, and use this to describe mixtures of gas and dark matter. We discuss how KFT can be applied to study cosmic structure formation with modified theories of gravity. As an example for an application to a non-cosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.