Probability distribution function of the aperture mass field with large deviation theory

TL;DR

This paper develops a theoretical model for the probability distribution of the aperture mass in cosmic shear surveys using large deviation theory, enabling more precise predictions and highlighting the need for improved simulations.

Contribution

It introduces a large deviation principle-based formalism for aperture mass statistics and proposes a nulling procedure to isolate specific redshift ranges, improving predictive accuracy.

Findings

Predictions for the one-point PDF of aperture mass are highly accurate.

Simulations currently lack the precision needed to match theoretical predictions.

Systematic effects like shape noise and lensing corrections are discussed for future surveys.

Abstract

In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected matter density field and more specifically to the angular aperture masses. The latter holds the advantage of being an observable that can be directly extracted from the observed shear field and to be, by construction, independent from the long wave modes. Furthermore we show that, with the help of a nulling procedure based on the so-called BNT transform, it is possible to build observables that depend only on a finite range of redshifts making them also independent from the small-scale modes. This procedure makes predictions for the shape of the one-point Probability Distribution Function of such an observable very accurate, comparable to what had been previously obtained for 3D observables. Comparisons with specific simulations reveal however inconsistent results showing that synthetic lensing maps were not accurate enough for such refined observables. It points to the need for more precise dedicated numerical developments whose performances could be benchmarked with such observables. We furthermore review the possible systematics that could affect such a formalism in future weak-lensing surveys like Euclid, notably the impact of shape noise as well as leading corrections coming from lens-lens couplings, geodesic deviation, reduced shear and magnification bias.