Wavelet Moments for Cosmological Parameter Estimation

TL;DR

This paper introduces invariant 3D wavelet moments as novel summary statistics for cosmological data analysis, significantly improving parameter constraints over traditional power spectrum methods.

Contribution

The paper presents a new set of wavelet-based summary statistics for cosmological matter fields that enhance parameter estimation accuracy in large-scale structure analysis.

Findings

Wavelet moments improve parameter constraints by a factor of 5 to 10.

They outperform the power spectrum baseline in Fisher forecast tests.

The method effectively captures non-Gaussian information in non-linear regimes.

Abstract

Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical and computational complexities, this remains one of the main challenges in analyzing observational data. We present a set of summary statistics for cosmological matter fields based on 3D wavelets to tackle this challenge. These statistics are computed as the spatial average of the complex modulus of the 3D wavelet transform raised to a power $q$ and are therefore known as invariant wavelet moments. The 3D wavelets are constructed to be radially band-limited and separable on a spherical polar grid and come in three types: isotropic, oriented, and harmonic. In the Fisher forecast framework, we evaluate the performance of these summary statistics on matter fields from the Quijote suite, where they are shown to reach state-of-the-art parameter constraints on the base $\Lambda$CDM parameters, as well as the sum of neutrino masses. We show that we can improve constraints by a factor 5 to 10 in all parameters with respect to the power spectrum baseline.