Kinetic Field Theory for Cosmic Structure Formation

TL;DR

This paper uses kinetic field theory to analyze non-linear cosmic structure formation, revealing universal asymptotic behaviors of power spectra and bispectra for density and velocity fluctuations across different models.

Contribution

It introduces a kinetic field theory approach to cosmic structure formation, demonstrating universal asymptotic power-law decay of spectra independent of cosmological details.

Findings

Power spectra decay as $k^{-3}$ for large wave numbers.

Bispectrum decays as $k^{-11/2}$ asymptotically.

Results are valid across various cosmological models and dark matter types.

Abstract

We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are drawn from a Gaussian random field. We place particular emphasis on the late-time, asymptotic behaviour on small spatial scales of low-order statistical measures for the distribution of particles in configuration and velocity space. Our main result is that the power spectra for density and velocity fluctuations in ensembles of particles freely streaming along Zel'dovich trajectories asymptotically fall off with wave number $k$ like $k^{-3}$ for $k\to\infty$, irrespective of the cosmological model and the type of dark matter assumed, with the exponent set only by the number of spatial dimensions. This conclusion remains valid for density-fluctuation power spectra if particle interactions are taken into account in a mean-field approximation. We also show that the bispectrum of freely-streaming particles falls off asymptotically like $k^{-11/2}$ under the same general conditions.