Modeling the Clustering of Dark-Matter Haloes in Resummed Perturbation Theories

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 (protohalo). We adopt a fluid-like description for the evolution of perturbations in the protohalo 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 to resum the power spectrum. For halo masses M < 1014 h-1 Msun, 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-1 approaching the requirements of future galaxy redshift surveys.