On the reach of perturbative methods for dark matter density fields

TL;DR

This paper investigates the effectiveness of perturbative methods in modeling dark matter density fields, demonstrating that including non-perturbative transformations improves accuracy and extends the validity of theoretical predictions.

Contribution

It introduces a full non-perturbative transformation from Lagrangian to Eulerian space that resums long wavelength motions, enhancing the match with non-linear density fields.

Findings

Achieves 1% accuracy in power spectrum up to k=0.25 h/Mpc at z=0

Extends the regime of validity of perturbative methods compared to standard approaches

Identifies stochastic contributions as a key source of residual errors

Abstract

We study the mapping from Lagrangian to Eulerian space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian displacements with Lagrangian Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard Eulerian Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regime of validity of this approach is expected to extend that of the Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z=0 the power spectrum of the density field is reproduced with an accuracy of 1 % (10 %) up to k=0.25 h/Mpc (k=0.46 h/Mpc). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as $k^4$ as it does in the very low-k regime. Thus, modeling this contribution might be challenging.