On the primordial information available to galaxy redshift surveys

TL;DR

This paper explores the limits of primordial information recovery from galaxy surveys, showing that existing algorithms extract nearly all accessible data and identifying factors that determine reconstruction noise and accuracy.

Contribution

It introduces a simplified model and linearized limit to analyze the effectiveness of reconstruction algorithms and explains the transition point where correlation drops sharply.

Findings

Reconstruction algorithms match the linear input field cross correlation coefficients.

The transition to no correlation is determined by the number of galaxies, not shot noise.

Linear scales allow mode reconstruction below shot noise levels with sufficient displacement constraints.

Abstract

We investigate the amount of primordial information that can be reconstructed from spectroscopic galaxy surveys, as well as what sets the noise in reconstruction at low wavenumbers, by studying a simplified universe in which galaxies are the Zeldovich displaced Lagrangian peaks in the linear density field. For some of this study, we further take an intuitive linearized limit in which reconstruction is a convex problem but where the solution is also a solution to the full nonlinear problem, a limit that bounds the effectiveness of reconstruction. The linearized reconstruction results in similar cross correlation coefficients with the linear input field as our full nonlinear algorithm. The linearized reconstruction also produces similar cross correlation coefficients to those of reconstruction attempts on cosmological N-body simulations, which suggests that existing reconstruction algorithms are extracting most of the accessible information. Our approach helps explain why reconstruction algorithms accurately reproduce the initial conditions up to some characteristic wavenumber, at which point there is a quick transition to almost no correlation. This transition is set by the number of constraints on reconstruction (the number of galaxies in the survey) and not by where shot noise surpasses the clustering signal, as is traditionally thought. We further show that on linear scales a mode can be reconstructed with precision well below the shot noise expectation if the galaxy Lagrangian displacements can be sufficiently constrained. We provide idealized examples of nonlinear reconstruction where shot noise can be outperformed.