Universal k^-d Small-Scale Scaling of the Cold-Dark-Matter Power Spectrum
For cold dark matter in d spatial dimensions, the nonlinear matter power spectrum P(k) approaches a universal k^-d power law at wavenumbers well above the nonlinear scale. The paper explains this non-perturbatively as gravitational turbulence: gravitational collapse drives a turbulent phase-space flow of the quadratic Casimir invariant in which the linear and nonlinear time scales balance, fixing the exponent in analogy with Batchelor passive-scalar turbulence. The same law is recovered by expressing P(k) as a kinetic-field-theory phase-space integral evaluated by the saddle-point method, and is confirmed by 1D Vlasov-Poisson simulations.
Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum Yonadav
A study of the small-scale limit of the cosmological matter power spectrum P(k), the Fourier transform of the density two-point correlation function. For cold dark matter in d spatial dimensions the …