Accuracy of analytical models of the large-scale matter distribution

TL;DR

This paper assesses the accuracy of analytical models for the large-scale matter distribution, combining perturbation theory and halo models to improve predictions of the matter power spectrum and correlation function.

Contribution

It demonstrates that reorganized perturbative expansions with Gaussian damping achieve percent accuracy at BAO scales, and analyzes the impact of halo model uncertainties on predictions.

Findings

Gaussian damping improves convergence and accuracy.

Lagrangian expansions are efficient at low orders.

Halo mass function uncertainty limits model precision.

Abstract

We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo model, we study the convergence rate of several perturbative expansion schemes and the impact of nonperturbative effects, as well as the sensitivity to phenomenological halo parameters. We check that the simple reorganization of the standard perturbative expansion, with a Gaussian damping prefactor, provides a well-ordered convergence and a finite correlation function that yields a percent accuracy at the baryon acoustic oscillation peak (as soon as one goes to second order). Lagrangian-space expansions are somewhat more efficient, when truncated at low orders, but may diverge at high orders. We find that whereas the uncertainty on the halo-profile mass-concentration relation is not a strong limitation, the uncertainty on the halo mass function can severely limit the accuracy of theoretical predictions for $P(k)$ (this also applies to the power spectra measured in numerical simulations). The real-space correlation function provides a better separation between perturbative and nonperturbative effects, which are restricted to $x \lesssim 10 h^{-1}$Mpc at all redshifts.