Abstract

The matter power spectrum is one of the fundamental quantities in the study of large-scale structure in cosmology. In this talk, I will describe its small-scale asymptotic limit, and give a theoretical argument to the effect that, for cold dark matter, P(k) has a universal asymptotic scaling with the wave-number k, for k >> k_nl, viz. P(k) ~ k^(-3). I will explain how gravitational collapse drives a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and non-linear time scales are balanced, and how this balance dictates the k dependence of the power spectrum. The coldness of the dark-matter distribution function — its non-vanishing only on a 3-dimensional sub-manifold of phase-space — underpins the analysis. I will show Vlasov-Poisson simulations that support the theory, and if time permits, also describe a stationary-phase technique for deriving an equivalent result.