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[astro-ph/0509418] Renormalized Cosmological Perturbation Theory
Authors:M. Crocce, R. Scoccimarro
Abstract:We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be written in a way that closely resembles the halo model.
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Anze Slosar

Joined: 24 Sep 2004
Posts: 205
Affiliation: Brookhaven National Laboratory

PostPosted: September 18 2005  Reply with quote

I would just like to draw you attention to this tour de force paper, presenting the perturbation theory from a fresh perspective. Basically, instead of doing the standard PT theory by considering powers in δ and θ, they express the final amplitude of a mode \mathbf{k} as a sum over vertices corresponding to coupling with \mathbf{k}_1 and \mathbf{k}-\mathbf{k}_1 at some time η'<η (now). Then they do some heavy butchery summing up these diagrams to get a much better behaved expansion than the standard PT. I am not an expert, but it sounds very promising to me. There is also a companion paper [astro-ph/0509419], but I haven't managed to get that far so far...
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