Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function

TL;DR

This paper introduces the Halo Zeldovich Perturbation Theory (HZPT), a model combining perturbation theory and halo modeling that accurately predicts dark matter clustering statistics across scales without free parameters.

Contribution

The paper develops the HZPT model that unifies perturbation theory and halo models, providing highly accurate predictions for the dark matter power spectrum and correlation function.

Findings

Achieves better than 1% accuracy for correlation function above 5 Mpc/h.

Predicts the power spectrum with 1% accuracy up to k ~ 1 h/Mpc.

Identifies two key halo scales: 1 Mpc/h and 26 Mpc/h.

Abstract

Perturbation theory for dark matter clustering has received a lot of attention in recent years, but its convergence properties remain poorly justified and there is no successful model that works both for correlation function and for power spectrum. Here we present Halo Zeldovich approach combined with perturbation theory (HZPT), in which we use standard perturbation theory at one loop order (SPT) at very low $k$, and connect it to a version of the halo model, for which we adopt the Zeldovich approximation plus a Pade expansion of a compensated one halo term. This low $k$ matching allows us to determine the one halo term amplitude and redshift evolution, both of which are in an excellent agreement with simulations, and approximately agree with the expected value from the halo model. Our Pade expansion approach of the one halo term added to Zeldovich approximation identifies two typical halo scales averaged over the halo mass function, the halo radius scale of order of 1Mpc/h, and the halo mass compensation scale of order 26Mpc/h. The model gives better than one percent accurate predictions for the correlation function above 5Mpc/h at all redshifts, without any free parameters. With three fitted Pade expansion coefficients the agreement in power spectrum is good to a percent up to $k \sim 1$h/Mpc, which can be improved to arbitrary $k$ by adding higher order terms in Pade expansion.