How well can (renormalized) perturbation theory predict dark matter clustering properties?

There has been some recent activity in trying to understand the dark matter clustering properties in the quasilinear regime, through resummation of perturbative terms, otherwise known as the renormalized perturbation theory [M. Crocce and R. Scoccimarro, Phys. Rev. D 73, 063519 (2006).], or the renormalization group method [P. McDonald, astro-ph/0606028.]. While it is not always clear why such methods should work so well, there is no reason for them to capture nonperturbative events such as shell-crossing. In order to estimate the magnitude of nonperturbative effects, we introduce a (hypothetical) model of sticky dark matter, which only differs from collisionless dark matter in the shell-crossing regime. This enables us to show that the level of nonperturbative effects in the dark matter power spectrum at $k\sim 0.1{\mathrm{Mpc}}^{-1}$, which is relevant for baryonic acoustic oscillations, is about a percent, but rises to order unity at $k\sim 1{\mathrm{Mpc}}^{-1}$.

Figure 1

Left: Halo model dark matter power spectrum for collisionless (solid) and sticky (dotted) dark matter. Right: Relative difference between power spectra of collisionless and sticky dark matter models. This shows the level of nonperturbative effects in the dark matter power spectrum.

Figure 2

The level of nonperturbative effects in the nonlinear power spectrum (see Fig. 1), as a function of nonlinear power.