[astro-ph/0610336] How well can (renormalized) perturbation theory predict dark matter clustering properties?

Authors:  Niayesh Afshordi (ITC, Harvard)
Abstract:  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}.
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Anze Slosar
Posts: 183
Joined: September 24 2004
Affiliation: Brookhaven National Laboratory

[astro-ph/0610336] How well can (renormalized) perturbation

Post by Anze Slosar » October 15 2006

This is quite an interesting paper that attempts to find the fundemental limit that any perturbative scheme could, in principle, achieve. I think that the idea of using sticky DM model is quite clever, but I am not sure about the execution. The halo model as a paradigm is based on standard N-body stuff, so to a certain extent you get out what you put in: it is to be expected that the two models will start to diverge when the 1-halo term kicks; in other words the result of this paper puts a lower limit on where the two cases would actually diverge... So, to do it properly, one would need to run an N-body with sticky particles (I think that something similar has already been done to treat star-formation - not sure if that stickiness is of the right sort)

Besides, how does this relate to the work done in astro-ph/0605012? I vaguelly remember talking to Peter Coles, who claimed that his approach survives shell-crossing (but I can't be asked to read 45 pages on Sunday :) )

Niayesh Afshordi
Posts: 49
Joined: December 17 2004
Affiliation: Perimeter Institute/ University of Waterloo

[astro-ph/0610336] How well can (renormalized) perturbation

Post by Niayesh Afshordi » October 15 2006

Anze, Thanks for your comment.

Doing a simulation of sticky DM was the first thing that came to my mind, but was not sure that it was worth the effort.

After I posted the preprint, Roya Mohayee reminded me that sticky DM is in fact very similar to the adhesion model, which is a way to continue Zeldovich approximation beyond shell crossing. Adhesion model is simply adding a tiny viscosity to the Euler equation to regularize caustics, without heating up the fluid. So I think it must be fairly easy to simulate.

However, I'm still not sure if it is worth doing a simulation in order to get an estimate of the error lower limit. As I say in the paper, on larger scales, the difference btw sticky and collisionless DM is dominated by the 2-halo term, which gives a rough estimate of the error if you screw things up in the virialized regions.

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