Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum

Abstract

The matter power spectrum, $P(k)$, is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in $d$ spatial dimensions, $P(k)$ has a universal $k^{-d}$ asymptotic scaling with the wave-number $k$, for $k\gg k_{\mathrm{nl}}$, where $k_{\mathrm{nl}}^{-1}$ denotes the length scale at which non-linearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a non-perturbative analysis of the system's phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and non-linear time scales are balanced, and this balance dictates the $k$ dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The $k^{-d}$ scaling is also derived by expressing $P(k)$ as a phase-space integral in the framework of kinetic field theory, which is analysed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function - its non-vanishing only on a $d$-dimensional sub-manifold of phase-space - underpins both approaches. The theory is accompanied by $1\mathrm{D}$ Vlasov-Poisson simulations, which confirm it.

arXiv commentSubmitted, comments welcome

References in corpus (42)

• A Universal Density Profile from Hierarchical Clustering
• Simulating the joint evolution of quasars, galaxies and their large-scale distribution
• First results from the IllustrisTNG simulations: matter and galaxy clustering
• The Inner Structure of LambdaCDM Halos III: Universality and Asymptotic Slopes
• Large-Scale Galaxy Bias
• Cosmological Non-Linearities as an Effective Fluid
• Evolution of structure in cold dark matter universes
• Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions
• Warm dark matter chills out: constraints on the halo mass function and the free-streaming length of dark matter with 8 quadruple-image strong gravitational lenses
• The Small-Scale Power Spectrum of Cold Dark Matter
• The power spectrum of SUSY-CDM on sub-galactic scales
• Separating the Early Universe from the Late Universe: cosmological parameter estimation beyond the black box
• Discontinuous Galerkin algorithms for fully kinetic plasmas
• Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence
• The Zeldovich approximation
• Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
• Galaxy Formation with BECDM -- II. Cosmic Filaments and First Galaxies
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• On Separate Universes
• Discreteness effects in cosmological N-body simulations
• Gravitational Instability of Cold Matter
• The halo model for cosmology: a pedagogical review
• Constraints on dark-matter properties from large-scale structure
• Inner cusps of the first dark matter haloes: Formation and survival in a cosmological context
• Constraining dark matter properties with Cosmic Microwave Background observations
• Dark Matter properties through cosmic history
• Conservative Discontinuous Galerkin Schemes for Nonlinear Fokker-Planck Collision Operators
• Post-collapse perturbation theory in 1D cosmology -- beyond shell-crossing
• A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics
• Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence
• Kinetic Field Theory: Exact free evolution of Gaussian phase-space correlations
• Asymptotic expansions for the Large Scale Structure
• A Universal Profile of the Dark Matter Halo and the Two-point Correlation Function
• A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory
• Phase-space structure analysis of self-gravitating collisionless spherical systems
• Kinetic Field Theory for Cosmic Structure Formation
• An Eulerian Perturbation Approach to Large Scale Structures: Extending the Adhesion Approximation
• Turbulence model of the cosmic structure
• On the asymptotic behaviour of cosmic density-fluctuation power spectra
• Multiple-Scales Approach to The Averaging Problem in Cosmology

Cited by in corpus (3)

• Prompt cusps in hierarchical dark matter halos: Implications for annihilation boost
• Variational autoencoder for generating realistic $N$-body simulations for dark matter halos
• Free Cosmic Density Bispectrum on Small Scales