Information escaping the correlation hierarchy of the convergence field in the study of cosmological parameters

TL;DR

This paper demonstrates that the hierarchy of moments of the convergence field quickly loses information on nonlinear scales, making it an incomplete and inefficient cosmological probe, but a logarithmic transformation can restore its effectiveness.

Contribution

The study reveals the rapid loss of information in the moment hierarchy of the convergence field and proposes a logarithmic mapping to recover its utility for cosmological parameter estimation.

Findings

Only 5% of Fisher information remains in the hierarchy at unit variance.

The hierarchy becomes incomplete and poor for nonlinear scales.

A logarithmic mapping restores the hierarchy's usefulness.

Abstract

Using fits to numerical simulations, we show that the entire hierarchy of moments quickly ceases to provide a complete description of the convergence one-point probability density function leaving the linear regime. This suggests that the full N-point correlation function hierarchy of the convergence field becomes quickly generically incomplete and a very poor cosmological probe on nonlinear scales. At the scale of unit variance, only 5% of the Fisher information content of the one-point probability density function is still contained in its hierarchy of moments, making clear that information escaping the hierarchy is a far stronger effect than information propagating to higher order moments. It follows that the constraints on cosmological parameters achievable through extraction of the entire hierarchy become suboptimal by large amounts. A simple logarithmic mapping makes the moment hierarchy well suited again for parameter extraction.