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, parameterfree 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 noncosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.

We present a new analytical description of baryonic matter in a cosmological framework, using the formalism of 'Kinetic Field Theory' (KFT) -a statistical field theory approach to structure formation based on the dynamics of classical particles. So far, only the purely gravitational dynamics of dark matter had been considered in KFT, but an accurate description of cosmic structure formation requires to also take into account the baryonic gas dynamics. In this paper, we propose to achieve this by incorporating an effective mesoscopic particle model of hydrodynamics into the recently developed framework of Resummed KFT. Our main result is the baryonic density contrast power spectrum computed to lowest perturbative order, assuming a simplified isothermal fluid model. Compared to the spectrum of dark matter, the baryonic spectrum shows a suppression of power as well as an oscillatory behaviour associated with sound waves on scales smaller than the Jeans length. We further compare our result to the linear spectrum of an isothermal fluid obtained from Eulerian perturbation theory (EPT), finding good quantitative agreement within the approximations we made in the EPT calculation. A subsequent paper will resolve the problem of coupling both dark and baryonic matter, to gain a full model of cosmic matter. Applying the mesoscopic particle approach to more general ideal or viscous fluids will also be subject of upcoming work.