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

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 lend-lens couplings, geodesic deviation, reduced shear and magnification bias.

Automated summary

A theoretical model for the one-point statistics of the aperture mass (Map) in tomographic cosmic shear surveys is developed using the large deviation principle applied to the projected matter density field and angular aperture masses. The nulling procedure based on the BNT transform can create observables independent of small-scale modes, making predictions for the probability distribution function of the observable very accurate. However, comparisons with simulations show inconsistent results, indicating the need for more precise numerical developments for refined observables in weak-lensing surveys like Euclid.