Modeling the clustering of dark-matter haloes in resummed perturbation theories

TL;DR

This paper develops an analytical model using resummed perturbation theory to accurately predict the clustering of dark-matter haloes, matching N-body simulations and aiding future galaxy survey analyses.

Contribution

It introduces a fluid-like perturbation approach with analytical resummation techniques to model halo clustering, improving accuracy over previous methods.

Findings

Good agreement with N-body simulations for halo masses below 10^{14} Msol/h

Achieves 5% accuracy in halo-matter cross spectrum up to k=0.1 h/Mpc at z=0

Extends perturbation theory to better predict galaxy clustering in future surveys

Abstract

We address the issue of the cosmological bias between matter and galaxy distributions, looking at dark-matter haloes as a first step to characterize galaxy clustering. Starting from the linear density field at high redshift, we follow the centre of mass trajectory of the material that will form each halo at late times (proto-halo). We adopt a fluid-like description for the evolution of perturbations in the proto-halo distribution, which is coupled to the matter density field via gravity. We present analytical solutions for the density and velocity fields, in the context of renormalized perturbation theory. We start from the linear solution, then compute one-loop corrections for the propagator and the power spectrum. Finally we analytically resum the propagator and we use a suitable extension of the time-renormalization-group method (Pietroni 2008) to resum the power spectrum. For halo masses M<10^{14} Msol/h our results at z=0 are in good agreement with N-body simulations. Our model is able to predict the halo-matter cross spectrum with an accuracy of 5 per cent up to k = 0.1 h/Mpc approaching the requirements of future galaxy redshift surveys.