Kinetic Field Theory for Cosmic Structure Formation

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.

64 pages, 25 figures, draft prepared for submission to La Rivista del Nuovo Cimento

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• Statistical Mechanics of Collisionless Orbits. V. The approach to equilibrium for idealized self-gravitating systems
• Gravitational Wave Signatures of Primordial Black Hole Reheating in Upcoming Interferometry Missions
• Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations
• Free Cosmic Density Bispectrum on Small Scales
• Kinetic field theory: effects of modified gravity theories with screening mechanisms on non-linear cosmic density fluctuations