On the reach of perturbative descriptions for dark matter displacement fields

TL;DR

This paper assesses the accuracy of Lagrangian Perturbation Theory (LPT) in modeling dark matter displacement fields by comparing it with N-body simulations, revealing a stochastic component that limits predictive precision.

Contribution

It introduces a measurement of the stochastic displacement term within the EFT framework, highlighting its impact on the accuracy of perturbative models for dark matter.

Findings

Detected a non-zero EFT coefficient.

Identified a stochastic displacement term.

Quantified a 1% error limit at specific scales.

Abstract

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding $N$-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors or transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a $1\%$ error on the non-linear power spectrum at $k=0.2 h$/Mpc at $z=0$. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.