Large deviations theory approach to cosmic shear calculations: the one-point aperture mass

TL;DR

This paper develops a formalism based on Large Deviations Theory to accurately compute the statistical properties of the aperture mass in cosmic shear, including the PDF and skewness, accounting for nonlinear effects.

Contribution

It extends the Large Deviation Principle to a broader class of observables in cosmology, providing a way to quantify the impact of common approximations on aperture mass statistics.

Findings

Derived the cumulant generating function and PDF of aperture mass.

Quantified the effect of neglecting nonlinear shear effects on skewness.

Reconstructed the one-point PDF of aperture mass with corrections.

Abstract

This paper presents a general formalism that allows the derivation of the cumulant generating function and one-point Probability Distribution Function (PDF) of the aperture mass ($\hat{M}_{ap}$), a common observable for cosmic shear observations. Our formalism is based on the Large Deviation Principle (LDP) applied, in such cosmological context, to an arbitrary set of densities in concentric cells. We show here that the LDP can indeed be used for a much larger family of observables than previously envisioned, such as those built from continuous and nonlinear functionals of the density profiles. The general expression of the observable aperture mass depends on reduced shear profile making it a rather involved function of the projected density field. Because of this difficulty, an approximation that is commonly employed consists in replacing the reduced shear by the shear in such a construction neglecting therefore non-linear effects. We were precisely able to quantify how this approximation affects the $\hat{M}_{ap}$ statistical properties. In particular we derive the corrective term for the skewness of the $\hat{M}_{ap}$ and reconstruct its one-point PDF.