An $n$-th order Lagrangian Forward Model for Large-Scale Structure

TL;DR

This paper introduces a comprehensive Lagrangian perturbation theory-based forward model for large-scale structure, accurately predicting matter and tracer distributions up to certain scales, validated against N-body simulations.

Contribution

It provides a complete, flexible forward model at arbitrary order in LPT, including bias operators and higher derivatives, applicable to any expansion history without simplifying assumptions.

Findings

Subpercent agreement with N-body simulations up to k~0.2 h/Mpc.

Accurate power spectrum and sigma_8 inference with effective sound speed.

Validated for matter and biased tracers, matching simulations across scales.

Abstract

A forward model of matter and biased tracers at arbitrary order in Lagrangian perturbation theory (LPT) is presented. The forward model contains the complete LPT displacement field at any given order in perturbations, as well as all relevant bias operators at that order and leading order in derivatives. The construction is done for any expansion history and does not rely on the Einstein-de Sitter approximation. A large subset of higher-derivative bias operators is also included. As validation test, we compare the $n$LPT-predicted matter density field and that from N-body simulations using the same initial conditions. For simulations using a cutoff in the initial conditions, we find subpercent agreement up to scales of $k\sim 0.2 h\,{\rm Mpc}^{-1}$. We also find subpercent agreement with full simulations without cutoff, both for the power spectrum and nonlinear $\sigma_8$-inference, when allowing for the effective sound speed. The application to biased tracers (halos) has already been presented in a recent paper (arXiv:2009.14176).