# Perturbation Theory for BAO reconstructed fields: one-loop results in real-space matter density field

## TL;DR

This paper calculates the one-loop power spectrum for reconstructed matter density fields using perturbation theory, showing that BAO reconstruction improves agreement with initial linear spectra and N-body simulations, especially at larger smoothing scales.

## Contribution

It provides the first one-loop perturbative analysis of BAO reconstructed fields, demonstrating the effectiveness of reconstruction in reducing nonlinear effects and non-Gaussianity.

## Key findings

- Reconstruction reduces one-loop power spectrum amplitude, aligning it closer to the linear spectrum.
- Agreement with N-body simulations improves after reconstruction at one-loop order.
- Reconstruction significantly decreases bispectrum amplitude, matching N-body results in the weakly nonlinear regime.

## Abstract

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian Baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decrease after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale $R_s$ larger than around 10$h^{-1}$Mpc. On smaller $R_s$,however, the deviation from the linear spectrum becomes significant on large scales ($k\lt R_s^{-1}$) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small $k$ after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.