Speaker
Description
The matter power spectrum, $P(k)$, is one of the fundamental quantities in the study of large-scale structure in cosmology. In this talk, I will study its small-scale asymptotic limit, and give a theoretical argument to the effect that, for cold dark matter in $d$ spatial dimensions, $P(k)$ has a universal $k^{-d}$ asymptotic scaling with the wave-number $k$, for $k \gg k_{\rm nl}$, where $k_{\rm nl}^{-1}$ denotes the length scale at which non-linearities in gravitational interactions become important. 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 this balance dictates the $k$ dependence of the power spectrum. The $k^{-d}$ scaling can also be derived by expressing $P(k)$ as a phase-space integral in the framework of kinetic field theory, analysing it 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. I will show Vlasov-Poisson simulations to support the theory.
