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 (astro-ph/0509418), or the renormalization group method (astro-ph/0606028). While it is not always clear why such methods should work so well, there is no reason for them to capture non-perturbative events such as shell-crossing. In order to estimate the magnitude of non-perturbative 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 non-perturbative effects in the dark matter power spectrum at k ~ 0.1 Mpc^{-1}, which is relevant for baryonic acoustic oscillations, is about a percent, but rises to order unity at k ~ 1 Mpc^{-1}.