Cosmic Structure Formation with Kinetic Field Theory

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, 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.

Relativistic kinetic gases as direct sources of gravity

“…Inserting λ = mφΣ proves the desired variation formula (35). The variation δ L λ = mδ L (φΣ), which comes from the change of L, is discussed during the derivation of the gravitational field equation coupled to the gas in Section IV and Appendix B.…”

“…A further interesting line of investigation is to study the relation of our description of the relativistic kinetic gas to the framework of kinetic field theory, which was recently applied to cosmology [35].…”

“…When we studied the variation of the action of the kinetic gas under manifold induced coordinate changes we claimed equation (35)…”

Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

“…Kinetic Field Theory (KFT) describes ensembles of classical particles in and out of equilibrium [1][2][3]. It is based upon the Martin-Siggia-Rose approach to classical statistical systems [4] and has been adapted to cosmological initial conditions and to the expanding cosmological background in previous papers [5,6]. Its central mathematical object is a generating functional encapsulating the statistical properties of the initial state, the Green's function or propagator of the equations of motion, and the particle-particle interactions.…”

General relativistic nonideal fluid equations for dark matter from a truncated cumulant expansion

“…These investigations range from ideal fluid dynamics [32,33], to second-order theories [34][35][36] and to the Einstein-Vlasov system of equations [37][38][39]. Further there have been investigations of effective fluid theories [40][41][42] and more recently a statistical field theory which maps to a nonequilibrium kinetic theory has been developed [43][44][45].…”