Nonlinear reconstruction

TL;DR

This paper introduces a direct nonlinear reconstruction method that nonparametrically recovers the linear density field from observed nonlinear data, enhancing the analysis of large scale structure surveys.

Contribution

It presents a novel multigrid algorithm for nonlinear reconstruction, extending linear displacement theory to fully nonlinear fields with minimal computational cost.

Findings

Successfully recovers linear initial conditions up to nonlinear scales

Achieves high correlation (>0.5) for scales up to k≈1 h/Mpc

Potentially improves information extraction from large scale structure surveys

Abstract

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale ($r_{\delta_r\delta_L}>0.5$ for $k\lesssim1\ h/\mathrm{Mpc}$) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping initiatives.