Optimizing the Recovery of Fisher Information in the Dark Matter Power Spectrum

TL;DR

This paper demonstrates that combining wavelet filtering and density reconstruction techniques significantly enhances the recovery of Fisher information in dark matter density fields, especially at small scales, with implications for cosmological parameter estimation.

Contribution

The study introduces a combined approach using Wavelet Non-Linear Wiener Filter and density reconstruction to improve Fisher information recovery in dark matter simulations, showing synergistic effects.

Findings

Fisher information plateau increases by over an order of magnitude at k > 1.0h/Mpc for particles.

Combined techniques outperform individual methods, with a recovery boost of 3-5 times.

Reconstruction has limited effect on halo catalogues, but wavelet filtering significantly boosts information.

Abstract

We combine two Gaussianization techniques - Wavelet Non-Linear Wiener Filter (WNLWF) and density reconstruction - to quantify the recovery of Fisher information that is lost in the gravitational collapse. We compute a displacement fields, in analogy with the Zel'dovich approximation, and apply a Wavelet Non-Linear Wiener Filter that decomposes the reconstructed density fields into a Gaussian and a non-Gaussian component. From a series of 200 realizations of N-body simulations, we compute the recovery performance for density fields obtained with both dark matter particles and haloes. We find that the height of the Fisher information trans-linear plateau is increased by more than an order of magnitude at k > 1.0h/Mpc for particles, whereas either technique alone offers an individual recovery boost of only a factor of three to five. We conclude that these two techniques work in a symbiosis, as their combined performance is stronger than the sum of their individual contribution. When applied to the halo catalogues, we find that the reconstruction has only a weak effect on the recovery of Fisher Information, while the non-linear wavelet filter boosts the information by about a factor offive. We also observe that non-Gaussian Poisson noise saturates the Fisher information, and that shot noise subtracted measurements exhibit a milder information recovery.