A critical look at cosmological perturbation theory techniques

TL;DR

This paper compares various analytic methods for predicting the non-linear matter power spectrum against high-resolution simulations, revealing their strengths, limitations, and the significance of higher-order corrections at different redshifts.

Contribution

It provides the first direct comparison of multiple analytic approaches with simulations and introduces 2-loop perturbation theory calculations for CDM models.

Findings

Analytic methods predict large-scale behavior well but fail at small scales.

2-loop perturbation theory improves agreement at high redshift.

Perturbation theory's reliability diminishes at low redshift and small scales.

Abstract

Recently a number of analytic prescriptions for computing the non-linear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus they must be compared with numerical simulations to assess their range of validity. We present a direct side-by-side comparison of several of these analytic approaches, using a suite of high-resolution N-body simulations as a reference, and discuss some general trends. All of the analytic results correctly predict the behavior of the power spectrum at the onset of non-linearity, and improve upon a pure linear theory description at very large scales. All of these theories fail at sufficiently small scales. At low redshift the dynamic range in scale where perturbation theory is both relevant and reliable can be quite small. We also compute for the first time the 2-loop contribution to standard perturbation theory for CDM models, finding improved agreement with simulations at large redshift. At low redshifts however the 2-loop term is larger than the 1-loop term on quasi-linear scales, indicating a breakdown of the perturbation expansion. Finally, we comment on possible implications of our results for future studies.