The cumulant generating function as a novel observable to cumulate weak lensing information

TL;DR

This paper introduces the cumulant generating function (CGF) as a new observable for weak lensing analysis, demonstrating it captures as much cosmological information as the traditional probability density function, with potential for multi-scale analysis.

Contribution

It is the first to show that the weak lensing CGF can serve as an effective observable, simplifying joint statistics computation and enhancing theoretical predictions in cosmology.

Findings

CGF captures equivalent cosmological information as the PDF.

Demonstrated the use of CGF in weak lensing as a novel observable.

Potential for multi-scale tomographic analysis in cosmology.

Abstract

Key non-Gaussian properties of cosmological fields can be captured by their one-point statistics, providing a complement to two-point statistical measurements from power spectra or correlation functions. Large deviation theory can robustly predict the one-point statistics of cosmological density fields on mildly non-linear scales from first principles. It provides a direct prediction for the cumulant generating function (CGF) of such fields, from which a prediction for the more commonly used probability density function (PDF) is extracted through an inverse Laplace transform. For joint one-point statistics of multiple fields, the inverse Laplace transform rapidly becomes more cumbersome and computationally expensive. In this work, we demonstrate for the first time that the weak lensing CGF itself can be used as an observable that captures an equal amount of cosmological information to the PDF. While we use the weak-lensing convergence field as a simplistic and instructive example, this work is intended as a first step towards a cosmological analysis based on large deviation theory in the context of a nulling framework, which excludes contributions from small scales to facilitate highly accurate theoretical predictions. In this context, the method should be generally applicable for a multi-scale tomographic analysis of weak lensing and galaxy clustering.